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Lowest Common Multiple Flashcards
GCSE Mathematics (Edexcel) 1MA1
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Lowest Common Multiple (LCM)
The smallest number that is a multiple of two or more numbers.
How to find the LCM using listing multiples
List the multiples of each number and identify the smallest multiple that appears in both lists.
How to find the LCM using prime factorisation
Write each number as a product of prime factors, then multiply the highest powers of all the prime factors together.
LCM of 4 and 6 (using listing multiples)
Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... LCM = 12.
LCM of 12 and 15 (using prime factorisation)
Prime factors: 12 = 2² × 3, 15 = 3 × 5. LCM = 2² × 3 × 5 = 60.
Why is the LCM useful?
The LCM is used to solve problems involving synchronisation, such as finding when two events will occur at the same time.
LCM of 8 and 14 (using listing multiples)
Multiples of 8: 8, 16, 24, 32, 40, 48, 56... Multiples of 14: 14, 28, 42, 56... LCM = 56.
LCM of 9 and 12 (using prime factorisation)
Prime factors: 9 = 3², 12 = 2² × 3. LCM = 2² × 3² = 36.
Difference between LCM and HCF
LCM is the smallest common multiple of two numbers, while HCF is the largest common factor of two numbers.
Real-life example of LCM
If two buses arrive at a stop every 12 minutes and 15 minutes, the LCM (60 minutes) tells you when they will arrive together.
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