Q5 of 56 Page 17

L.C.M of two numbers is 14 times their H.C.F. The sum of L.C.M and H.C.F is 600.

If one number is 280 find the other?

According to the given condition

L.C.M = 14 X, H.C.F + L.C.M = 600, 1 NUMBER= 280


Let the H.C.F (a,b) = X where a = 280 and b = ?


But H.C.F + L.C.M = 600


⇒ X + 14X = 600


⇒ 15X = 600


⇒


⇒ X = 40


⇒ H.C.F = 40


⇒ L.C.M = 14 X


⇒ 14 × 40= 560


Also H.C.F × L.C.M = 1ST NUMBER × 2ND NUMBER


⇒ 40 × 560 = 280 × b



⇒ b = 40 × 2


⇒ b = 80


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