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Difficulty: EasyHCF and LCM

Consider the three fractions 125\frac{12}{5}, 247\frac{24}{7}, and 3611\frac{36}{11}. What is the exact value of their Least Common Multiple (LCM)?

Answer: 72

Answer

The Least Common Multiple (LCM) of the given fractions is 72.
To find the Least Common Multiple (LCM) of a set of fractions, we must divide the LCM of their numerators by the HCF of their denominators. The numerators (1212, 2424, and 3636) have an LCM of 7272. The denominators (55, 77, and 1111) share no common factors other than 11, making their HCF 11. Thus, the final LCM is 72/1=7272 / 1 = 72.

Step-by-Step Solution

1
State the standard formula for finding the LCM of multiple fractions.
LCM = (LCM of numerators) / (HCF of denominators).
This mathematical property governs how multiples apply to rational numbers.
2
Calculate the LCM of the numerators.
The LCM of 1212, 2424, and 3636 is 7272.
7272 is the smallest integer perfectly divisible by all three numerators.
3
Calculate the HCF of the denominators.
The HCF of 55, 77, and 1111 is 11.
The numbers 55, 77, and 1111 are prime and share no common factors other than 11.
4
Compute the final fraction LCM.
72÷1=7272 \div 1 = 72.
Dividing the computed numerator LCM by the denominator HCF yields the answer.

Key Concept

Calculating the LCM of fractions using the specific formula relating numerators and denominators.
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Topics

HCF and LCM

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