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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

Combine the factors, eliminating duplicates.

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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Q: Solve HCF and LCM problems by prime factorization?
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The Highest Common Factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the HCF of 120 and 400, you can use the prime factorization method. The prime factorization of 120 is 2^3 * 3 * 5 and the prime factorization of 400 is 2^4 * 5^2. To find the HCF, you take the common prime factors with the lowest exponent, which in this case is 2^3 * 5 = 40. Therefore, the HCF of 120 and 400 is 40.


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As a product of its prime factors: 2*5*7 = 70 Note that at least two or more numbers are needed to find their HCF


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