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Difficulty: EasyHCF and LCM

The product of two positive integers is 21602160 and their Highest Common Factor (HCF) is 1212. What is their Least Common Multiple (LCM)?

Answer: 180

Answer

180
For any two positive integers, the product of their Highest Common Factor (HCF) and Least Common Multiple (LCM) is always equal to the product of the numbers themselves. Given that the product is 21602160 and the HCF is 1212, the LCM is calculated by rearranging the formula to LCM=ProductHCF\text{LCM} = \frac{\text{Product}}{\text{HCF}}. Substituting the values gives 2160÷12=1802160 \div 12 = 180.

Step-by-Step Solution

1
Identify the fundamental formula connecting HCF, LCM, and the product of two positive integers.
HCF×LCM=Product\text{HCF} \times \text{LCM} = \text{Product}
This relationship allows you to find one missing value when the other two are known.
2
Substitute the known values from the problem into the equation.
12×LCM=216012 \times \text{LCM} = 2160
The problem explicitly states that the product is 21602160 and the HCF is 1212.
3
Solve for the LCM by dividing both sides of the equation by 1212.
LCM=180\text{LCM} = 180
Isolating the LCM variable provides the final requested value.

Key Concept

Relationship between the product of two numbers and their HCF and LCM
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Topics

HCF and LCM

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