What is the Least Common Multiple of 112 and 132?
Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.
Least common multiple (LCM) of 112 and 132 is 3696.
LCM(112,132) = 3696
Least Common Multiple of 112 and 132 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 112 and 132, than apply into the LCM equation.
GCF(112,132) = 4
LCM(112,132) = ( 112 × 132) / 4
LCM(112,132) = 14784 / 4
LCM(112,132) = 3696
Least Common Multiple (LCM) of 112 and 132 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 112 and 132. First we will calculate the prime factors of 112 and 132.
Prime Factorization of 112
Prime factors of 112 are 2, 7. Prime factorization of 112 in exponential form is:
112 = 24 × 71
Prime Factorization of 132
Prime factors of 132 are 2, 3, 11. Prime factorization of 132 in exponential form is:
132 = 22 × 31 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 112 and 132.
LCM(112,132) = 24 × 71 × 31 × 111
LCM(112,132) = 3696
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Related Least Common Multiples of 132
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