Relation between HCF and LCM
For two positive integers a and b, the product of the numbers equals the product of their HCF and LCM.
Practice This ConceptMain explanation
Teacher explanation
This relation is a quick check in exam questions. Once the HCF is known, the LCM can be found quickly, and the relation also helps verify whether a final answer is reasonable. It works for two positive integers.
Example
If the numbers are 18 and 30, then 18 x 30 = 6 x 90.
Simple analogy
Product splits into HCF and LCM by division.
Common confusion
Students divide by the wrong value or try to apply the relation to more than two numbers at once.
Exam tip
Use this relation as a shortcut after finding either the HCF or the LCM by factorisation.
Answer writing and exam use
1-mark use
Write the exact meaning of relation between hcf and lcm in one clean line.
2-mark use
Define relation between hcf and lcm and add one example or condition.
3-mark use
Explain relation between hcf and lcm, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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