What is the Least Common Multiple of 1056 and 1074?
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 1056 and 1074 is 189024.
LCM(1056,1074) = 189024
Least Common Multiple of 1056 and 1074 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1056 and 1074, than apply into the LCM equation.
GCF(1056,1074) = 6
LCM(1056,1074) = ( 1056 × 1074) / 6
LCM(1056,1074) = 1134144 / 6
LCM(1056,1074) = 189024
Least Common Multiple (LCM) of 1056 and 1074 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 1056 and 1074. First we will calculate the prime factors of 1056 and 1074.
Prime Factorization of 1056
Prime factors of 1056 are 2, 3, 11. Prime factorization of 1056 in exponential form is:
1056 = 25 × 31 × 111
Prime Factorization of 1074
Prime factors of 1074 are 2, 3, 179. Prime factorization of 1074 in exponential form is:
1074 = 21 × 31 × 1791
Now multiplying the highest exponent prime factors to calculate the LCM of 1056 and 1074.
LCM(1056,1074) = 25 × 31 × 111 × 1791
LCM(1056,1074) = 189024
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