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