Page 69 - ICSE Math 5

Least Common Multiple (L.C.M.)
Top Tip
The Least Common Multiple or L.C.M. of two or more • The product of two prime
numbers is their smallest common multiple. numbers give their L.C.M.

We can find the L.C.M. of the given numbers either by • If the smaller number in
the given two numbers is a
listing method or by common division method.
factor of the greater number,
Example 17: Find the L.C.M. of 18 and 36 using listing then the greater number
method. will be the L.C.M. of the two
numbers.
Solution: Step 1: List the multiples of 18 and 36.
Multiples of 18 = 18, 36 , 54, 72 , …

Multiples of 36 = 36 , 72 , 108, 144, …

Step 2: Compare and identify the common multiples of 18 and 36 that appear in
the list.
36 and 72 are the two common multiples of 18 and 36.

Step 3: Write the L.C.M. of 18 and 36.
So, the L.C.M. of 18 and 36 is 36.

Example 18: Find the L.C.M. of 42, 64 and 72 by common division method. 2 42, 64, 72
Solution: Step 1: Write 42, 64 and 72 in a row separated by commas. 2 21, 32, 36

Step 2: Divide all or at least one of the given numbers by the 2 21, 16, 18
smallest prime number. If only one number can be 2 21, 8, 9
divided by that prime number, then bring down the 2 21, 4, 9
other numbers as it is. 2 21, 2, 9
Step 3: Repeat the method till all the numbers are reduced 3 21, 1, 9
to 1 in the last row. 3 7, 1, 3
Step 4: Multiply all the prime numbers that are on the left 7 7, 1, 1
column to find the L.C.M. 1, 1, 1

So, the L.C.M. of 42, 64 and 72 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 = 4,032.

Exercise 5.3

1. Find the H.C.F. of the following numbers by listing method.
(a) 72 and 84 (b) 16, 18 and 24 (c) 80, 165 and 190

2. Find the H.C.F. of the following numbers by common division method.

(a) 56 and 78 (b) 142, 304 and 560 (c) 912, 216 and 400

3. Find the L.C.M. of the following numbers by listing method.
(a) 7 and 35 (b) 55 and 105 (c) 20, 50 and 100

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