What is the Least Common Multiple of 390 and 408?
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 390 and 408 is 26520.
LCM(390,408) = 26520
Least Common Multiple of 390 and 408 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 390 and 408, than apply into the LCM equation.
GCF(390,408) = 6
LCM(390,408) = ( 390 × 408) / 6
LCM(390,408) = 159120 / 6
LCM(390,408) = 26520
Least Common Multiple (LCM) of 390 and 408 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 390 and 408. First we will calculate the prime factors of 390 and 408.
Prime Factorization of 390
Prime factors of 390 are 2, 3, 5, 13. Prime factorization of 390 in exponential form is:
390 = 21 × 31 × 51 × 131
Prime Factorization of 408
Prime factors of 408 are 2, 3, 17. Prime factorization of 408 in exponential form is:
408 = 23 × 31 × 171
Now multiplying the highest exponent prime factors to calculate the LCM of 390 and 408.
LCM(390,408) = 23 × 31 × 51 × 131 × 171
LCM(390,408) = 26520
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