Page 51 - Math Skill - 5
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Factors and Multiples 49
Step 3: Multiply all the factors and the numbers in the last row to get the LCM.
LCM of 12, 16 and 20 = 2 × 2 × 2 × 2 × 3 × 5 = 240
Properties of LCM and HCF
HCF of two prime numbers is 1. HCF of two consecutive numbers is 1.
HCF of given numbers cannot be greater than any one of the given numbers.
HCF of two co-prime numbers is always 1.
LCM of given numbers cannot be less than any of the given numbers.
LCM of two co-primes is equal to their product.
Product of two numbers is equal to the product of the HCF and LCM.
For any two numbers A and B, HCF × LCM = A × B.
Let’s Attempt
Example 1: Find the LCM of 30, 40 and 50.
Solution: 2 30, 40, 50
5 15, 20, 25
2 3, 4, 5
2 3, 2, 5
3 3, 1, 5
5 1, 1, 5
1, 1, 1 LCM of 30, 40 and 50 = 2 × 5 × 2 × 2 × 3 × 5 = 600
Example 2: HCF and LCM of 24 and another number are 8 and 120 respectively. Find the
other number.
Solution: We know that, HCF × LCM = One number × Other number
8 × 120 = 24 × Other number
8 120×
Other number = = 8 × 5 = 40
24
The other number is 40.
Exercise 4.4
1. Find the LCM of the following numbers.
(a) 50, 65 (b) 48, 80, 96 (c) 60, 72, 90, 108
(d) 18, 27, 36, 63 (e) 75, 125, 375 (f) 100, 125, 600
2. Find the HCF and LCM of the numbers and verify whether their product is equal to the
product of the numbers.
(a) 75, 125 (b) 108, 144 (c) 110, 1331
(d) 510, 190 (e) 750, 165 (f) 777, 888
