Page 42 - Math 7

Operations on Whole Numbers

Find the L.C.M of 28, 30, and 35

2 28, 30, 35 2 is the least common prime factor of 28 and 30.
5 14, 15, 35 5 is the least common prime factor of 15 and 35.
7 14, 3, 7 7 is the least prime factor of 14 and 7.
2, 3, 1

? L.C.M. = 2 × 5 × 7 × 2 × 3 = 420

Workedout examples

Example 1: Write the sets of a few multiples of 6, 9, and 12. Make a set of their
common multiples and find their L.C.M.
Solution:
Here, M = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, …}
(6)
M = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …}
(9)
M (12) = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120, …}
Now, M ˆ M ˆ M = (36, 72, …)
(6) (9) (12)
? L.C.M. of 6, 9, and 12 is 36.
Example 2: Three measuring rods are 30 cm, 45 cm, and 60 cm long. Find the
shortest length of cloth which can be measured exactly by any one
of these rods.
Solution:
Here, the shortest length of the cloth is the L.C.M. of 30 cm, 45 cm, and 60 cm.

2 30, 45, 60
3 15, 45, 30
5 5, 15, 10
1, 3, 2

? L.C.M. = 2 × 3 × 5 × 3 × 2 = 180
Hence, the required shortest length of the cloth is 180 cm.
Example 3: Find the least number which leaves a remainder 7 when it is divided
by any one of the numbers 20, 30, and 40.
Solution:
Here, the least number divisible by 20, 30, and 40 is their L.C.M. Then, the required
least number = (L.C.M. of 20, 30, 40) + 7.

2 20, 30, 40
2 10, 15, 20
5 5, 15, 10
1, 3, 2
? L.C.M. = 2 × 2 × 5 × 3 × 2 = 120
Hence, the required least number = 120 + 7 = 127.

Vedanta Excel in Mathematics - Book 7 40 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur