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NCERT Solutions for Class 7th Maths Chapter 3 In-text Questions — Least, but not Last!

Book page 55 Updated on2026-09-19

Q1.
Anshu and Guna make torans out of strips of cloth. Multiple strips are placed one next to another to make a toran. Anshu uses strips of length 6 cm and Guna uses strips of 8 cm length. If both have to make torans of the same length, what is the smallest possible length, the torans could be? What is the length of the shortest toran that they can both make?
Answer

The shortest common length is 24 cm.

Anshu's torans (multiples of 6): 6, 12, 18, 24, 30, 36, 42, 48, 54, …
Guna's torans (multiples of 8): 8, 16, 24, 32, 40, 48, 56, 64, 72, …
Common multiples: 24, 48, 72, …
Lowest common multiple = 24 cm

Anshu uses 24 ÷ 6 = 4 strips; Guna uses 24 ÷ 8 = 3 strips.

Why it happens: Anshu can only build lengths that are whole numbers of 6 cm strips, so his toran is always a multiple of 6. Guna's is always a multiple of 8. For the two torans to be the same length, that length must be a multiple of both — a common multiple. The shortest one is the lowest common multiple.
Tip: 24 is the Lowest Common Multiple (LCM) of 6 and 8.
Q2.
What about the largest common multiple? Does such a number exist?
Answer

No. There is no largest common multiple.

Common multiples of 6 and 8: 24, 48, 72, 96, 120, 144, …
Whatever common multiple you name, add 24 to it
The new number is still a multiple of 6 and still a multiple of 8
So it is a bigger common multiple
Why it happens: the multiples of a number go on forever, and so do the common multiples — they are exactly the multiples of the LCM. A never-ending increasing list has a smallest member but no largest one. That is why we speak of the lowest common multiple and the highest common factor, and never the other way round: the list of common factors is finite (nothing bigger than the numbers themselves), so it has a greatest member.
Q3.
A sweet shop gives out free gajak to school children on Mondays. Today is a Monday and Kabamai enjoyed eating the gajak. But she visits the sweet shop once every 10 days. When is the next time she would be able to get free gajak from Sweet shop? (Answer in number of days.)
Answer

After 70 days.

Free gajak days (Mondays, multiples of 7): 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, …
Kabamai's visits (multiples of 10): 10, 20, 30, 40, 50, 60, 70, …
First day common to both lists = 70
LCM(7, 10) = 7 × 10 = 70

70 days is 10 weeks, and also Kabamai's 7th visit.

Why it happens: the shop gives gajak only on days that are multiples of 7 from today, and Kabamai comes only on days that are multiples of 10. The two must line up, so the day has to be a common multiple. The next such day is the lowest common multiple. Since 7 and 10 have no common prime factor, their LCM is simply their product.
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