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Lowest common multiple (LCM)
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EasyQuestion 1
[2 marks]Find the lowest common multiple (LCM) of 6 and 8.
Solution for Question 1
MediumQuestion 2
[3 marks]Using prime factorisation, find the LCM of 18 and 24.
Solution for Question 2
HardQuestion 3
[4 marks]Two buses leave the station at 9:00 am. Bus A returns every 12 minutes. Bus B returns every 18 minutes.
(a) At what time will both buses next be at the station together?
(b) How many times will they be at the station together between 9:00 am and 12:00 noon (including 9:00 am)?
Solution for Question 3
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The Lowest Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. For smaller numbers, list multiples of each until you find the first one they share.
For larger numbers, use prime factorisation: write each number as a product of primes, then multiply together ALL primes that appear, using the highest power of each. This is the opposite of HCF where you use the lowest powers.
LCM is useful for adding fractions (finding common denominators), scheduling problems (when will events coincide?), and problems about repeating patterns. Remember: HCF × LCM = product of the two numbers, which can be a useful check.
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