What is the Least Common Multiple of 9900 and 9919?
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 9900 and 9919 is 98198100.
LCM(9900,9919) = 98198100
Least Common Multiple of 9900 and 9919 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9900 and 9919, than apply into the LCM equation.
GCF(9900,9919) = 1
LCM(9900,9919) = ( 9900 × 9919) / 1
LCM(9900,9919) = 98198100 / 1
LCM(9900,9919) = 98198100
Least Common Multiple (LCM) of 9900 and 9919 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 9900 and 9919. First we will calculate the prime factors of 9900 and 9919.
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
Prime Factorization of 9919
Prime factors of 9919 are 7, 13, 109. Prime factorization of 9919 in exponential form is:
9919 = 71 × 131 × 1091
Now multiplying the highest exponent prime factors to calculate the LCM of 9900 and 9919.
LCM(9900,9919) = 22 × 32 × 52 × 111 × 71 × 131 × 1091
LCM(9900,9919) = 98198100
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