HCF & LCM from Prime Factors (Year 10)
Free printable UK Year 10 (GCSE Foundation) maths worksheet: use prime factorisations to find the HCF and LCM of two numbers, the unique-factorisation method.
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Grade 9 · Math worksheet
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Math
HCF & LCM from Prime Factors
Use prime factorisations (written in index notation) to find the HCF (lowest shared power of each common prime) and LCM (highest power of every prime present) of each pair of numbers.
- 1.Write 15 and 297 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 15 and 297.
- 2.Write 44 and 18 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 44 and 18.
- 3.Write 99 and 22 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 99 and 22.
- 4.Write 77 and 91 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 77 and 91.
- 5.Write 24 and 297 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 24 and 297.
- 6.Write 175 and 15 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 175 and 15.
- 7.Write 20 and 175 as products of their prime factors, then use them to find (a) the HCF, (b) the LCM of 20 and 175.
- 8.A = 2³ × 11 and B = 7 × 11 (A = 88, B = 77). Using these prime factorisations, find the HCF and LCM of A and B.
- 9.A = 2² × 3² and B = 3 × 7 (A = 36, B = 21). Using these prime factorisations, find the HCF and LCM of A and B.
- 10.A = 2³ × 3³ and B = 3 × 5 (A = 216, B = 15). Using these prime factorisations, find the HCF and LCM of A and B.
- 11.A = 5 × 11 and B = 11 × 13 (A = 55, B = 143). Using these prime factorisations, find the HCF and LCM of A and B.
- 12.A = 3² × 7 and B = 3² × 11 (A = 63, B = 99). Using these prime factorisations, find the HCF and LCM of A and B.
- 13.A = 7 × 11 and B = 3 × 11 (A = 77, B = 33). Using these prime factorisations, find the HCF and LCM of A and B.
- 14.For 63 and 54, the HCF is 9 and the LCM is 378. Verify that HCF x LCM = 63 x 54, and state whether this is true.
- 15.For 28 and 200, the HCF is 4 and the LCM is 1400. Verify that HCF x LCM = 28 x 200, and state whether this is true.
- 16.For 325 and 10, the HCF is 5 and the LCM is 650. Verify that HCF x LCM = 325 x 10, and state whether this is true.
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