Page 56 - Start Up Mathematics_5

Example 16: Find the HCF of 90, 108 and 126 by long division method.

Solution: Step 1: Find the HCF of any two of the three given numbers.

Step 2: Find the HCF of the third 1 7
remaining number and the HCF 90 1 0 8 18 1 2 6
found in step 1. This will be the – 9 0 5 – 1 2 6
HCF of all the given numbers. 1 8 9 0 0
HCF of 90 and 108 is 18. – 9 0
HCF of 126 and 18 is 18. 0

So, the HCF of 90, 108 and 126 is 18.
Similarly, to find the HCF of more than three numbers, we keep finding the HCF of the
remaining numbers and the HCF of the previous numbers to find the final HCF.

EXERCISE 3.3

1. Find the HCF of the following numbers using prime factorization.
(a) 72 and 84 (b) 45 and 180 (c) 36 and 150

(d) 24, 60 and 140 (e) 108, 264 and 324 (f) 80, 120 and 200

2. Find the HCF of the following numbers by long division method.
(a) 32 and 68 (b) 56 and 78 (c) 96 and 218
(d) 48, 70 and 130 (e) 95, 105 and 315 (f) 142, 304 and 560

Least Common Multiple (LCM)

LCM of two or more numbers is the smallest or least common multiple of the given numbers,
which is divisible by each of the numbers.
Example 17: Find the LCM of 8 and 12.

Solution: Multiples of 8 = 8 16 24 32 40 48 56 64 72 80 …
Multiples of 12 = 12 24 36 48 60 72 84 96 108 120 …

Common multiples of 8 and 12 are 24, 48, 72, … .
Out of these the smallest common multiple is 24.
So, the LCM of 8 and 12 = 24

Example 18: Find the LCM of 24 and 36.

Solution: Multiples of 24 = 24 48 72 96 120 144 …
Multiples of 36 = 36 72 108 144 180 216…
Common multiples of 24 and 36 are 72, 144 … .

Out of these the smallest common multiple is 72.
So, the LCM of 24 and 36 = 72

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