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The LCM of two numbers A and B = AB ÷ F, where F is the GCF
For this question, AB = 270 x 9 = 2430
We now need to find a set of paired factors of 2430 such that both numbers are divisible by 9. So, just taking one of the pair as being a multiple of 9 then :-
270 x 9......Yes
135 x 18....Yes
90 x 27......Yes
67.5 x 36....No
54 x 45......Yes.........which is as far as we need to check.
So there are four pairs of numbers satisfying the given conditions : 270 & 9, 135 & 18, 90 & 27 and 45 & 54.
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How do you find the LCM using GCF?
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.
Can the GCF of two different numbers is the LCM of the numbers?
No, the only way the GCF and LCM of two numbers can be the same is if the numbers are the same.
What is the product of the GCF and LCM of two numbers?
The product of the GCF and LCM of a pair of numbers is equal to the product of the numbers.
How do you find two numbers if HCF and LCM are known?
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.
What is the LCM of 2 numbers that is 24 and the gcf is 12?
If the GCF of two numbers is 12 and the LCM is 24, the two numbers are 12 and 24.
