Question

The LCM and HCF of 45, 75 and 30 will be _ and _ respectively.​

• A. 1, 15
• B. 450, 30
• C. 75, 30
• D. 450, 15

Answer 1

The correct option is D 450, 15

LCM or HCF of three numbers is nothing but LCM or HCF of one of those numbers and LCM or HCF of the remaining two numbers.
Prime factorisation:
45 = 3 x 3 x 5
75 = 3 x 5 x 5
30 = 2 x 3 x 5
HCF of 45 and 75 = 3 x 5 = 15
Product of numbers = Product of HCF and LCM
So, LCM x 15 = 45 x 75
LCM = 225
HCF of 3 x 5 and 2 x 3 x 5 = 3 x 5 = 15
LCM of 3 x 3 x 5 x 5 and 2 x 3 x 5 = 2 x 3 x 3 x 5 x 5 = 450
HCF and LCM of 45, 75 and 30 are 15 and 450 respectively.