What is the Least Common Multiple of 678 and 690?
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 690 is 77970.
LCM(678,690) = 77970
Least Common Multiple of 678 and 690 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 690, than apply into the LCM equation.
GCF(678,690) = 6
LCM(678,690) = ( 678 × 690) / 6
LCM(678,690) = 467820 / 6
LCM(678,690) = 77970
Least Common Multiple (LCM) of 678 and 690 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 678 and 690. First we will calculate the prime factors of 678 and 690.
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 690
Prime factors of 690 are 2, 3, 5, 23. Prime factorization of 690 in exponential form is:
690 = 21 × 31 × 51 × 231
Now multiplying the highest exponent prime factors to calculate the LCM of 678 and 690.
LCM(678,690) = 21 × 31 × 1131 × 51 × 231
LCM(678,690) = 77970
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