What is the Least Common Multiple of 678 and 691?
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 678 and 691 is 468498.
LCM(678,691) = 468498
Least Common Multiple of 678 and 691 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 678 and 691, than apply into the LCM equation.
GCF(678,691) = 1
LCM(678,691) = ( 678 × 691) / 1
LCM(678,691) = 468498 / 1
LCM(678,691) = 468498
Least Common Multiple (LCM) of 678 and 691 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 678 and 691. First we will calculate the prime factors of 678 and 691.
Prime Factorization of 678
Prime factors of 678 are 2, 3, 113. Prime factorization of 678 in exponential form is:
678 = 21 × 31 × 1131
Prime Factorization of 691
Prime factors of 691 are 691. Prime factorization of 691 in exponential form is:
691 = 6911
Now multiplying the highest exponent prime factors to calculate the LCM of 678 and 691.
LCM(678,691) = 21 × 31 × 1131 × 6911
LCM(678,691) = 468498
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