Example: 30 and 42
Factor them.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
Select the common factors.
2 x 3 = 6, the GCF
Select the highest amount of each factor.
2 x 3 x 5 x 7 = 210, the LCM
Check it.
30 x 42 = 1260
210 x 6 = 1260
It checks.
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The GCF of two numbers multiplied by their LCM will equal the product of the original numbers. If you know the GCF, divide it into the product of the two. The result will be the LCM. If the GCF of two numbers is 1, the LCM is their product.
To make this easier, let's first factor 18 and 21 into their prime factors: 18=2*3^2 21=3*7 Now it's very easy to find the LCM and GCF. The LCM is 2*3^2*7=126, and the GCF is 3.
You need at least two numbers to find a GCF or an LCM and the LCM of those numbers can never be less than the GCF. 12 and 360 have a GCF of 12 and an LCM of 360. So do 60 and 72.
The product of the GCF and the LCM of two numbers is equal to the product of the original two numbers. Multiply the GCF and the LCM. The original two numbers will be another factor pair of that total. Find the factor pair that has that GCF and LCM.
2 and 5 are coprime integers: they do not have any common factors. Therefore the GCF is 1 and the LCM is their product, 2x5=10.