Find the LCM of 72, 80 and 252 using the prime factor method and the common division method.
Answers
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PRIME FACTORISATION
List all prime factors for each number.
Prime Factorization of 72 is:
2 x 2 x 2 x 3 x 3 => 2³ x 3²
Prime Factorization of 80 is:
2 x 2 x 2 x 2 x 5 => 2⁴ x 5¹
Prime Factorization of 252 is:
2 x 2 x 3 x 3 x 7 => 2² x 3² x 7¹
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 2, 3, 3, 5, 7
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7 = 5040
In exponential form:
LCM = 2⁴ x 3² x 5¹ x 7¹ = 5040
LCM = 5040
Therefore,
LCM(72, 80, 252) = 5040
COMMON DIVISION METHOD
Bring down any numbers that are not evenly divisible by the prime number.
When the last row of results is all 1's you are done.
Find the product of the prime numbers in the first column to get the LCM:
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 x 7
LCM = 5040
Therefore,
LCM(72, 80, 252) = 5040
