What is the Least Common Multiple of 16789 and 16800?
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 16789 and 16800 is 282055200.
LCM(16789,16800) = 282055200
Least Common Multiple of 16789 and 16800 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16789 and 16800, than apply into the LCM equation.
GCF(16789,16800) = 1
LCM(16789,16800) = ( 16789 × 16800) / 1
LCM(16789,16800) = 282055200 / 1
LCM(16789,16800) = 282055200
Least Common Multiple (LCM) of 16789 and 16800 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 16789 and 16800. First we will calculate the prime factors of 16789 and 16800.
Prime Factorization of 16789
Prime factors of 16789 are 103, 163. Prime factorization of 16789 in exponential form is:
16789 = 1031 × 1631
Prime Factorization of 16800
Prime factors of 16800 are 2, 3, 5, 7. Prime factorization of 16800 in exponential form is:
16800 = 25 × 31 × 52 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 16789 and 16800.
LCM(16789,16800) = 1031 × 1631 × 25 × 31 × 52 × 71
LCM(16789,16800) = 282055200
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