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27 Oct 2022, 10:56
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Given that LCM of positive integer m and n is 120, and m:n=3:4 and we need to find what is the greatest common factor(GCF) of m and n
\(\frac{m}{n}\) = \(\frac{3}{4}\) = \(\frac{3x}{4x}\)
where x was a common factor in m and n which got cancelled out. (x is also the GCF which we are looking for)
=> m = 3x and n = 4x
=> LCM(m,n) = x * 3 * 4 (As x was the common factor and 3 and 4 are the non-common factors) = 12x = 120 (given)
=> x = \(\frac{120}{12}\) = 10
=> GCF(x,y) = 10
So , Answer will be D
Hope it helps!
To learn more about LCM and GCD watch the following videos
\(\frac{m}{n}\) = \(\frac{3}{4}\) = \(\frac{3x}{4x}\)
where x was a common factor in m and n which got cancelled out. (x is also the GCF which we are looking for)
=> m = 3x and n = 4x
=> LCM(m,n) = x * 3 * 4 (As x was the common factor and 3 and 4 are the non-common factors) = 12x = 120 (given)
=> x = \(\frac{120}{12}\) = 10
=> GCF(x,y) = 10
So , Answer will be D
Hope it helps!
To learn more about LCM and GCD watch the following videos
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10 Aug 2025, 23:32
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M:N = 3:4 MCM (M y N) = 120
M = 3x4x10
N = 3x4x10
MCD = 10
D
M = 3x4x10
N = 3x4x10
MCD = 10
D
