I started to answer this in the comments box below, but both the question and the answer seems far too important for a mere comments box reflection:
Tom asked the question whether Liturgy of the Hours were really necessary to the pursuit of holiness. My long answer follows. My short answer is undoubtedly (and most assuredly from a personal, experiential perspective), "Yes it is." As difficult as it may be to fit into a life, whatever life it is fit into is made better by the discipline of following this great work of the Church.
With the advent of works like Magnificat a version of the litrugy tailored to those with strong time constraints is available to all. Moreover, as the name implies the "Liturgy of the Hours" is the work of the whole body of the church. It is liturgical prayer second in importance only to the Mass itself. Finally, the liturgy of the hours provides structure to the day. It would seem, to instill the discipline necessary to start the practice of the presence of God.
Personal prayer, while commendable, and indeed sanctifying often tends to be somewhat loosely regarded and on-the-fly. The Liturgy serves to structure this otherwise rather free-form mode of expression.
That's not to say you can't become holy without with Liturgy--but rather that the liturgy is so helpful to the process that it should not be remanded to a mere recommendation, but put forth as a sacred treasure whose usage greatly increases the probability of success on the road to holiness by virtue of the grace of obedience and discipline.
Finally, to address the objection, " After all, people in the world do not always have the luxury of living as though they occupied a cloister," I quote from the work of the Holy Father regarding lay participation in the Liturgy of the Hours.
Apostolic Letter Novo Millenio Inuente #34
John Paul II
It is therefore essential that education in prayer should become in some way a key-point of all pastoral planning. I myself have decided to dedicate the forthcoming Wednesday catecheses to reflection upon the Psalms, beginning with the Psalms of Morning Prayer with which the public prayer of the Church invites us to consecrate and direct our day. How helpful it would be if not only in religious communities but also in parishes more were done to ensure an all-pervading climate of prayer. With proper discernment, this would require that popular piety be given its proper place, and that people be educated especially in liturgical prayer. Perhaps it is more thinkable than we usually presume for the average day of a Christian community to combine the many forms of pastoral life and witness in the world with the celebration of the Eucharist and even the recitation of Lauds [Morning Prayer] and Vespers [Evening Prayer]. The experience of many committed Christian groups, also those made up largely of lay people, is proof of this. [emphasis added]
and from Sacrosanctum Concilium
from Sacrosanctum Concilium
83. Christ Jesus, high priest of the new and eternal covenant, taking human nature, introduced into this earthly exile that hymn which is sung throughout all ages in the halls of heaven. He joins the entire community of mankind to Himself, associating it with His own singing of this canticle of divine praise.
For he continues His priestly work through the agency of His Church, which is ceaselessly engaged in praising the Lord and interceding for the salvation of the whole world. She does this, not only by celebrating the eucharist, but also in other ways, especially by praying the divine office.
84. By tradition going back to early Christian times, the divine office is devised so that the whole course of the day and night is made holy by the praises of God. Therefore, when this wonderful song of praise is rightly performed by priests and others who are deputed for this purpose by the Church's ordinance, or by the faithful praying together with the priest in the approved form, then it is truly the voice of the bride addressed to her bridegroom; lt is the very prayer which Christ Himself, together with His body, addresses to the Father.
85. Hence all who render this service are not only fulfilling a duty of the Church, but also are sharing in the greatest honor of Christ's spouse, for by offering these praises to God they are standing before God's throne in the name of the Church their Mother. . . .
88. Because the purpose of the office is to sanctify the day, the traditional sequence of the hours is to be restored so that once again they may be genuinely related to the time of the day when they are prayed, as far as this may be possible. Moreover, it will be necessary to take into account the modern conditions in which daily life has to be lived, especially by those who are called to labor in apostolic works.
and this, from "Instructions on the Liturgy of the Hours"
27. Lay groups gathering for prayer, apostolic work, or any other reason are encouraged to fulfill the Church's duty,  by celebrating part of the liturgy of the hours. The laity must learn above all how in the liturgy they are adoring God the Father in spirit and in truth;  they should bear in mind that through public worship and prayer they reach all humanity and can contribute significantly to the salvation of the whole world. 
Finally, it is of great advantage for the family, the domestic sanctuary of the Church, not only to pray together to God but also to celebrate some parts of the liturgy of the hours as occasion offers, in order to enter more deeply into the life of the Church. 
It would seem to me far easier to become holy if one were to spend some time "sanctifying" and "consecrating" the day with the form of prayer specifically designed for that purpose.
For additional comments see here (Cardinal Spellman, 1950), John Paul II, 2001, and John Paul II, 2001