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FINDING THE LEAST COMMON MULTIPLE – LCM - REFERENCE
LEAST COMMON MULTIPLE (LCM) – the smallest number that is a multiple of two or more numbers.
There are two strategies that we can use to find the least common multiple.
STRATEGY #1 – LISTING MULTIPLES
1) List the multiples of each number.
2) Circle the first number that they have in common.
EXAMPLE #1: Find the LCM of 4 and 6.
Multiples of 4: 4,
8, 12, 16, 20, 24, 28, 32 …
Multiples of 6: 6,
12, 18, 24, 30 …
The Least Common
Multiple (LCM) = 12
EXAMPLE #2: Find the LCM of 9 and 27.
Multiples of 9: 9,
18, 27, 36, 45, 54, 63, 72, 81 …
Multiples of 27: 27,
54, 81…
TURN OVER
The Least Common
Multiple (LCM) = 27
Strategy #2 - LCM’s Cake Method
1) Draw a “cake layer” and place the numbers inside.
2) Find a common factor for the inside numbers. Place the common factor outside the cake layer.
3) Divide the inside numbers by the common factor. Place the answer(s) underneath each number and
draw a new cake layer.
4) Repeat steps until the bottom cake layer has numbers that are prime or have no common factors.
5) Circle the outside numbers and the numbers at the bottom cake layer forming an “L” shape.
6) Multiply these numbers to get the LCM.
EXAMPLE #1: Find the LCM of 72 and 96
2
6
2
72
96
48
36
8
6
4
3
2 × 6 × 2 × 4 × 3 = 288. Your LCM is 288
LCM SPECIAL SCENARIOS
 If you have two prime numbers, multiply them to find the LCM
 If you have one prime and one composite, check to see if they have a common factor, if they do not, multiply
the two numbers. If they do have a common factor, then follow the Cake Method Rules
EXAMPLE #2: Find the LCM of 12, 14, and 16
2
12
2
14
16
6
7
8
3
7
4
2 × 2 × 3 × 7 × 4 = 336. Your LCM is 336.
Since 7 is prime, you just carry it
to the next cake layer and look for
common factor for 6 and 8.