Question

Find the GCF and the LCM of the following numbers 1116,1674, 2728

Answer 1

Given the numbers;

`1116,1674,2728​`

We can find the GCF and LCM using the prime factors method below;

Part A: GCF

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainders.

In this case, we would compare the common prime factors that we get.

Thus;

`\begin{gathered} 1116=2^2*3^2*31 \\ 1674=2^1*3^3*31 \\ 2728=2^3*11*31 \end{gathered}`

By comparison, the value common across all three numbers is 2(once) and 31(once). Therefore the GCF is

`2*31=62`

Answer A:

`GCF=62`

Part B: LCM

The Least Common Multiple ( LCM ) . For three integers a,b,c denoted LCM(a,b,c), the LCM is the smallest positive integer that is evenly divisible by both a, b and c.

In this case, we would list all the prime numbers found, as many times as they occur most often for anyone given number, and multiply them together to find the LCM.

`\begin{gathered} 1116=2^2*3^2*31 \\ 1674=2^1*3^3*31 \\ 2728​=2^3*11*31 \end{gathered}`

Therefore the LCM would give;

`\text{LCM}=2^3*3^3*11*31=73656`

Answer B:

`\text{LCM}=73656`