Page 50 - Math Skill - 5

48 Maths

Exercise 4.3

1. Find the HCF of the following using prime factorisation method.
(a) 25, 175 (b) 16, 80 (c) 100, 500

(d) 210, 525 (e) 85, 240 (f) 144, 132 and 120
2. Find the HCF by long division method.
(a) 11, 13 (b) 17, 19 (c) 27, 31
(d) 121, 132 (e) 288, 216 (f) 900, 1125 and 1350

Lowest Common Multiple (LCM)
Let us consider the numbers 4 and 6 and find the multiples of both the numbers.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, ...
Multiples of 6 are 6, 12, 18, 24, 30, 36, ...
The common multiples are 12, 24, 36, ...

Out of these common multiples, 12 is the multiple which is the lowest (least).
Lowest Common Multiple: This smallest number that can be divided by the given numbers
without leaving any remainder is called the lowest common multiple.

Lowest common multiple is also called the least common multiple and is written as LCM.
We can find the LCM by two methods.
(a) Prime factorisation method (b) Common division method

LCM by Prime Factorisation

In this method, we first list the prime factors of the numbers and then multiply the common
factors and the remaining prime factors.
For example, find the LCM of 18 and 24.

Prime factors of 18 = 2 × 3 × 3
Prime factors of 24 = 2 × 2 × 2 × 3

Multiplying the common factors 2 and 3 and the remaining prime factors, we get.
LCM = 2 × 3 × 3 × 2 × 2 = 72.

LCM by Common Division Method

In this method, we follow the steps given below:
Let us consider the numbers 12, 16 and 20. 2 12, 16, 20

Step 1: Divide by the smallest prime number, which can divide at least 2 6, 8, 10
2
3,
4,
5
one of the numbers and bring down the numbers that cannot be 2 3, 2, 5
divided further. 3 3, 1, 5
Step 2: Continue divide by the smallest possible prime numbers, till 5 1, 1, 5
the last row contains prime numbers or co-prime numbers or 1. 1, 1, 1