What is the Least Common Multiple of 56 and 76?
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 56 and 76 is 1064.
LCM(56,76) = 1064
Least Common Multiple of 56 and 76 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 56 and 76, than apply into the LCM equation.
GCF(56,76) = 4
LCM(56,76) = ( 56 × 76) / 4
LCM(56,76) = 4256 / 4
LCM(56,76) = 1064
Least Common Multiple (LCM) of 56 and 76 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 56 and 76. First we will calculate the prime factors of 56 and 76.
Prime Factorization of 56
Prime factors of 56 are 2, 7. Prime factorization of 56 in exponential form is:
56 = 23 × 71
Prime Factorization of 76
Prime factors of 76 are 2, 19. Prime factorization of 76 in exponential form is:
76 = 22 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 56 and 76.
LCM(56,76) = 23 × 71 × 191
LCM(56,76) = 1064