0580/13 Oct/Nov 2022, Question 22: HCF and LCM
Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 4 marks
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The question, in short
Use the prime factor form 120 = 2ᵐ × 3 × 5 to find m, then find when two lights with periods 120 s and 144 s next turn red together after 10 00.
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Part (a) · 1 mark
Find the exponent m in the prime factorisation 120 = 2ᵐ × 3 × 5.
- 1120 = 2 × 2 × 2 × 3 × 5 = 2³ × 3 × 5, so m = 3
Answer3
Part (b) · 3 marks
Two lights change to red every 120 seconds and every 144 seconds, both at 10 00. Find the next time they change together.
- 1144 = 2⁴ × 3², 120 = 2³ × 3 × 5
- 2LCM = 2⁴ × 3² × 5 = 720 seconds
- 3720 seconds = 12 minutes
- 410 00 + 12 minutes = 10 12
Answer10 12
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Also searched as: 0580/13/O/N/22 · 0580_w22_qp_13 · 0580 w22 13 · question 22.
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