Quick answer: For two positive integers a and b, HCF(a,b) × LCM(a,b) = ab. The formula is for two numbers; do not extend this product identity directly to three numbers.
Worked example
Find the LCM of 18 and 24 given their HCF is 6.
- Compute the product 18×24 = 432.
- Divide by HCF: LCM = 432/6 = 72.
- 72/18 = 4 and 72/24 = 3.
Check the result
Prime factors give 18 = 2×3² and 24 = 2³×3. Taking highest powers gives 2³×3² = 72.
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Common mistake to avoid
An alleged HCF must divide both numbers. An alleged LCM must be divisible by both; use these as quick validity checks.
Try it yourself
1. Find LCM of 12 and 20 if HCF is 4. 2. Two numbers have HCF 3, LCM 30 and one number 6; find the other.
Answers and reasoning
1. 240/4 = 60. 2. 3×30/6 = 15; HCF(6,15) = 3 and LCM = 30.
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