How do you find the HCF and LCM of fractions such as 2/3, 8/9 and 16/81?
HCF of fractions = HCF of numerators / LCM of denominators; LCM of fractions = LCM of numerators / HCF of denominators. For 2/3, 8/9, 16/81 the HCF is 2/81 and the LCM is 16/3.
Explain it simply
The HCF of fractions is the biggest fraction that fits a whole number of times into each one. To make it big, take a big numerator (the HCF of the numerators) and keep the denominator just large enough to divide neatly (the LCM of the denominators). The LCM is the smallest fraction that each one fits into a whole number of times, so the roles flip.
Example
Question: Find the HCF and LCM of 2/3, 8/9 and 16/81.
Numerators: 2, 8, 16. Denominators: 3, 9, 81.
- HCF of numerators = 2. LCM of denominators = 81. HCF = 2/81.
- LCM of numerators = 16. HCF of denominators = 3. LCM = 16/3.
Check the HCF: (2/3) / (2/81) = 27, (8/9) / (2/81) = 36, (16/81) / (2/81) = 8. All whole numbers.
Check the LCM: (16/3) / (2/3) = 8, (16/3) / (8/9) = 6, (16/3) / (16/81) = 27. All whole numbers.
Every check gives a whole number, so both answers are right.
What to say in the interview
"HCF of fractions is HCF of the tops over LCM of the bottoms, and LCM of fractions is LCM of the tops over HCF of the bottoms. Always reduce each fraction to lowest terms first. Here that gives 2/81 and 16/3, and dividing each fraction by them gives whole numbers."
Common mistakes
- Not reducing fractions to lowest terms before applying the rule.
- Swapping the rules for HCF and LCM.