What is the Least Common Multiple of 12780 and 12800?
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 12780 and 12800 is 8179200.
LCM(12780,12800) = 8179200
Least Common Multiple of 12780 and 12800 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12780 and 12800, than apply into the LCM equation.
GCF(12780,12800) = 20
LCM(12780,12800) = ( 12780 × 12800) / 20
LCM(12780,12800) = 163584000 / 20
LCM(12780,12800) = 8179200
Least Common Multiple (LCM) of 12780 and 12800 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 12780 and 12800. First we will calculate the prime factors of 12780 and 12800.
Prime Factorization of 12780
Prime factors of 12780 are 2, 3, 5, 71. Prime factorization of 12780 in exponential form is:
12780 = 22 × 32 × 51 × 711
Prime Factorization of 12800
Prime factors of 12800 are 2, 5. Prime factorization of 12800 in exponential form is:
12800 = 29 × 52
Now multiplying the highest exponent prime factors to calculate the LCM of 12780 and 12800.
LCM(12780,12800) = 29 × 32 × 52 × 711
LCM(12780,12800) = 8179200
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