The sum of two numbers is 84 and their HCF is 12. If the ratio of their LCM to their HCF is 12:1, what are the two numbers?
Show answer & explanation
Correct answer: A
Explanation
Given:
Sum of two numbers = 84
HCF = 12
LCM : HCF = 12 : 1
Formula:
Numbers = 12x and 12y (where HCF = 12)
LCM = 12xy
LCM / HCF = 12
(12xy) / 12 = 12
xy = 12
Sum of numbers = 12x + 12y = 84
x + y = 7
x + y = 7
xy = 12
x = 3, y = 4
Numbers
= 12 × 3 = 36
= 12 × 4 = 48
Numbers = 36 and 48