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Difficulty: MediumHCF and LCM

Calculate the lowest common multiple (LCM) of the fractions 34\frac{3}{4}, 910\frac{9}{10}, and 1516\frac{15}{16}. Express your final answer as a decimal.

Answer: 22.5

Answer

22.5
The lowest common multiple (LCM) of a set of fractions is found by dividing the LCM of their numerators by the highest common factor (HCF) of their denominators. For the numerators 33, 99, and 1515, the LCM is 4545. For the denominators 44, 1010, and 1616, the HCF is 22. Thus, the LCM of the fractions is 452\frac{45}{2}, which equals 22.522.5 in decimal form.

Step-by-Step Solution

1
Recall the mathematical formula for finding the LCM of multiple fractions.
LCM of fractions=LCM of numeratorsHCF of denominators\text{LCM of fractions} = \frac{\text{LCM of numerators}}{\text{HCF of denominators}}
This formula is the standard method to determine the lowest common multiple when dealing with fractional values.
2
Identify the numerators and calculate their lowest common multiple (LCM).
The numerators are 33, 99, and 1515. Their LCM is 4545 (since 4545 is the smallest number perfectly divisible by 33, 99, and 1515).
The numerator of the final fraction requires the LCM of all the given numerators.
3
Identify the denominators and calculate their highest common factor (HCF).
The denominators are 44, 1010, and 1616. Their HCF is 22 (since 22 is the largest number that divides 44, 1010, and 1616 without a remainder).
The denominator of the final fraction requires the HCF of all the given denominators.
4
Apply the calculated values to the fraction LCM formula.
LCM=452\text{LCM} = \frac{45}{2}
Combining the results from the previous steps yields the LCM in fractional form.
5
Convert the resulting fraction into a decimal format.
452=22.5\frac{45}{2} = 22.5
The question explicitly requires the final answer to be expressed as a decimal.

Key Concept

Calculating the LCM of fractions using the specific formula: LCM of numerators divided by the HCF of denominators.
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Topics

HCF and LCM

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