Two numbers are in the ratio 3 : 5. Their LCM is 75. What is their HCF?
Two numbers are in the ratio 3 : 5
let the numbers be 3x and 5x
LCM (3x,5x) = 15x
given LCM = 75
15x = 75
$$ x = \frac{75}{15} $$
x = 5
numbers are 15 and 25
product of two numbers = product of LCM and HCF
$$ 15 \times 25 = 75 \times HCF $$
solving HCF = 5
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