2. What is the ‘Lowest Common
Multiple’?
• It is the lowest of the common multiples
of any numbers.
• So, we make lists of the multiples of
both numbers and take the first number
which appears in both lists.
3. There are 2 methods2 methods to find the
Lowest Common Multiple (L.C.M):
1.The old method.
2.The new method which is better.
4. 1. The old method
a) Write the list of multiples of every number
b) Take the common multiples
c) Choose the lowest
5. For example:
• Find the Lowest Common Multiple (L.C.M.) of 1010
and 15.15.
• A)A) List the multiples of both numbers:List the multiples of both numbers:
– Multiples of 10Multiples of 10 →→ 10, 20,10, 20, 3030, 40, 50,, 40, 50, 6060, 70, 80,, 70, 80, 9090……
– Multiples of 15Multiples of 15 →→ 15,15, 3030, 45,, 45, 6060, 75,, 75, 9090……
6. • B) Take the common multiples:B) Take the common multiples:
– Common multiples →→ 3030 –– 6060 –– 90…90…
• C) Choose the lowest:C) Choose the lowest:
– TheThe llowestowest ccommonommon mmultiple of 10 and 15 isultiple of 10 and 15 is 3030
– →→ L.C.M. (10, 15) = 30L.C.M. (10, 15) = 30
8. 2) The new method
a) Break down both numbers into their prime
factors.
b) Take all the factors.
c) If a factor is repeated, take the one with the
highest exponent.
9. For example:
• Find the Lowest Common Multiple (L.C.M.) of
3030 and 8.8.
A. Break down both numbers into their prime factors.
30 │30 │ 22 8 │8 │ 22
15 │15 │ 33 4 │4 │ 22
5 │5 │ 55 2 │2 │ 22
1 │1 │ 1 │1 │
10. B) Take all the factors.
• 30 = 2 · 3 · 5
• 8 = 2 · 2 · 2 = 2³
C) If a factor is repeated, take the one with the
highest exponent.
• 2³ has a higherhigher exponent than 2 so, we take 2³2³.
• →→L.C.M. (30, 8) = 3 · 5 ·L.C.M. (30, 8) = 3 · 5 · 2³2³ = 120= 120