HCF & LCM · Topic 6 of 6

➗ Fractions & Reciprocals

2 exam question types, fully solved

HCF and LCM also work on fractions. There are exactly two formulas to carry, plus one neat trick for adding reciprocals. Memorise which part goes on top and these are free marks.

The two fraction formulas (and a reciprocal shortcut)

• HCF of fractions .

• LCM of fractions .

Always reduce each fraction to lowest terms first. Sanity check: the HCF of fractions is the smallest value, the LCM the largest.

• Sum of reciprocals of two numbers: . Since , this becomes — plug straight in, never solve for the numbers.

⚖️HCF & LCM MachineSame prime factors — lowest powers make the HCF, highest powers make the LCM

and

HCF of numerators: HCF(4, 6) = 2 LCM of denominators: LCM(5, 25) = 25

HCF=HCF(4, 6)LCM(5, 25)=225

LCM of numerators: LCM(4, 6) = 12 HCF of denominators: HCF(5, 25) = 5

LCM=LCM(4, 6)HCF(5, 25)=125

HCF = 2/25 · LCM = 12/5

Memory hook: HCF is the small one → HCF on top, over LCM. LCM is the big one → LCM on top, over HCF.

HCF of and , so the denominator is .

Q1The HCF of 1/2 and 3/4 is:

Q2The LCM of 2/3 and 4/9 is:

Q3Two numbers sum to 24 with HCF 4 and LCM 20. Sum of reciprocals is:

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Real exam questions — Fractions & Reciprocals

2 question types · 8 solved examples from real SSC papers

For fractions: HCF = HCF(numerators)/LCM(denominators), LCM = LCM(numerators)/HCF(denominators). Sum of reciprocals = sum ÷ (HCF × LCM).

How to solve this type

Always reduce each fraction to lowest terms first. Then: HCF of fractions

=\dfrac{\text{HCF of numerators}}{\text{LCM of denominators}}

, and LCM of fractions

=\dfrac{\text{LCM of numerators}}{\text{HCF of denominators}}

. Sanity check: the HCF of fractions is the smallest, the LCM the largest.

The HCF of $\dfrac{4}{5}$ and $\dfrac{8}{15}$ is:

\dfrac{4}{5}

\dfrac{4}{15}

\dfrac{8}{15}

\dfrac{8}{5}

Find the LCM of $\dfrac{3}{7}$ and $\dfrac{9}{14}$ .

\dfrac{27}{14}

\dfrac{3}{7}

\dfrac{9}{7}

\dfrac{9}{14}

Find the HCF of $\dfrac{3}{4}$ and $\dfrac{9}{16}$ .

\dfrac{3}{16}

\dfrac{9}{16}

\dfrac{9}{4}

\dfrac{3}{4}

The LCM of $\dfrac{5}{8}$ , $\dfrac{15}{16}$ and $\dfrac{25}{24}$ is:

\dfrac{75}{2}

\dfrac{75}{24}

\dfrac{75}{8}

\dfrac{25}{8}