What is the Least Common Multiple of 31914 and 31920?
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 31914 and 31920 is 169782480.
LCM(31914,31920) = 169782480
Least Common Multiple of 31914 and 31920 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31914 and 31920, than apply into the LCM equation.
GCF(31914,31920) = 6
LCM(31914,31920) = ( 31914 × 31920) / 6
LCM(31914,31920) = 1018694880 / 6
LCM(31914,31920) = 169782480
Least Common Multiple (LCM) of 31914 and 31920 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 31914 and 31920. First we will calculate the prime factors of 31914 and 31920.
Prime Factorization of 31914
Prime factors of 31914 are 2, 3, 197. Prime factorization of 31914 in exponential form is:
31914 = 21 × 34 × 1971
Prime Factorization of 31920
Prime factors of 31920 are 2, 3, 5, 7, 19. Prime factorization of 31920 in exponential form is:
31920 = 24 × 31 × 51 × 71 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 31914 and 31920.
LCM(31914,31920) = 24 × 34 × 1971 × 51 × 71 × 191
LCM(31914,31920) = 169782480
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