4. The product of HCF and LCM of 60,84 and 108 is
a) 55360
b) 35360
c) 45500
d) 45360
Answers
Given:
60, 84 and 108
To find:
Product of HCF and LCM of 60,84, and 108.
Solution:
Three numbers 60,84 and 108 are given. Factors of 60, 84 and 108 are given below:
60 = 2×2×3×5 = 2²×3×5
84 = 2×2×3×7 = 2²×3×7
108 = 2×2×3×3×3 = 2²×3³
LCM (least common multiple) is the smallest number that is a multiple of all the numbers.
HCF (highest common factor) is the highest number of all the common factors among the numbers.
LCM = 2²×3³×5×7 = 3780
HCF = 2²×3 = 12
Product of LCM and HCF = 3780 × 12 = 45360
The product of HCF and LCM of 60, 84 and 108 is 45360.
Option (d) is the correct answer.
Answer:
45360
Step-by-step explanation:
Three numbers 60,84 and 108 are given. Factors of 60, 84 and 108 are given below:
60 = 2×2×3×5 = 2²×3×5
84 = 2×2×3×7 = 2²×3×7
108 = 2×2×3×3×3 = 2²×3³
LCM (least common multiple) is the smallest number that is a multiple of all the numbers.
HCF (highest common factor) is the highest number of all the common factors among the numbers.
LCM = 2²×3³×5×7 = 3780
HCF = 2²×3 = 12
Product of LCM and HCF = 3780 × 12 = 45360
The product of HCF and LCM of 60, 84 and 108 is 45360.