What is the Least Common Multiple of 9894 and 9900?
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 9894 and 9900 is 16325100.
LCM(9894,9900) = 16325100
Least Common Multiple of 9894 and 9900 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9894 and 9900, than apply into the LCM equation.
GCF(9894,9900) = 6
LCM(9894,9900) = ( 9894 × 9900) / 6
LCM(9894,9900) = 97950600 / 6
LCM(9894,9900) = 16325100
Least Common Multiple (LCM) of 9894 and 9900 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9894 and 9900. First we will calculate the prime factors of 9894 and 9900.
Prime Factorization of 9894
Prime factors of 9894 are 2, 3, 17, 97. Prime factorization of 9894 in exponential form is:
9894 = 21 × 31 × 171 × 971
Prime Factorization of 9900
Prime factors of 9900 are 2, 3, 5, 11. Prime factorization of 9900 in exponential form is:
9900 = 22 × 32 × 52 × 111
Now multiplying the highest exponent prime factors to calculate the LCM of 9894 and 9900.
LCM(9894,9900) = 22 × 32 × 171 × 971 × 52 × 111
LCM(9894,9900) = 16325100
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