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The L.C.M of two positive integers is thrice the larger number and the difference of the smaller number and the H.C.F is 12. The smaller number is:1. 182. 123. 164. 8 |
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Answer» Correct Answer - Option 1 : 18 Given: L.C.M = 3 × larger number Smaller number – H.C.F = 12 Formula used: The Product of H.C.F and L.C.M of any two numbers is equal to the product of that numbers. Calculation: Let, a = smaller number and b = larger number L.C.M of a, b = 3 × b = 3b a – H.C.F = 12, H.C.F = a – 12 Using formula, L.C.M × H.C.F = a × b ⇒ 3b × (a – 12) = ab ⇒ 3ab – 36b = ab ⇒ 2ab = 36b a = 36/2 = 18 ∴ Smaller number = 18 |
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