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Zorluk: KolayHCF and LCM

Determine the exact decimal value of the Least Common Multiple (LCM) for the two fractions 35\frac{3}{5} and 910\frac{9}{10}.

Cevap: 1.8

Cevap

1.8
To find the LCM of fractions, we use the standard formula: LCM(numerators) / HCF(denominators). The numerators are 3 and 9, and their LCM is 9. The denominators are 5 and 10, and their HCF is 5. Dividing the LCM of the numerators by the HCF of the denominators gives 9/5. Converting this fraction to a decimal yields exactly 1.8.

Adım Adım Çözüm

1
Identify the correct formula for finding the LCM of fractions.
LCM of fractions = LCM(numerators) / HCF(denominators)
This is the fundamental rule for calculating the least common multiple when dealing with rational numbers.
2
Calculate the Least Common Multiple of the numerators.
The numerators are 3 and 9. Their LCM is 9.
9 is the smallest integer that is perfectly divisible by both 3 and 9.
3
Calculate the Highest Common Factor of the denominators.
The denominators are 5 and 10. Their HCF is 5.
5 is the largest integer that perfectly divides both 5 and 10 without leaving a remainder.
4
Apply the formula and convert the resulting fraction to a decimal.
LCM = 9 / 5 = 1.8
The question specifically asks for the exact decimal value, so the fraction 9/5 must be converted to 1.8.

Anahtar Kavram

The Least Common Multiple (LCM) of a set of fractions is found by dividing the LCM of their numerators by the HCF of their denominators.
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Konular

HCF and LCM

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