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1. Two numbers are in the ratio 3 : 4. The product of their HCF and LCM is 2028. The sum of the numbers is = ?
∴ HCF = x
LCM = 3 × 4 × x = 12x
given that = HCF × LCM
=> x × 12x = 2028
=> 12x2 = 2028
=> x2 = 169
=> x = 13
∴ sum of numbers
= 3x + 4x
= 7x
= 7 × 13
= 91
Solution:
Let the numbers are = 3x, 4x respectively∴ HCF = x
LCM = 3 × 4 × x = 12x
given that = HCF × LCM
=> x × 12x = 2028
=> 12x2 = 2028
=> x2 = 169
=> x = 13
∴ sum of numbers
= 3x + 4x
= 7x
= 7 × 13
= 91