The least common multiple can be found by multiplying the highest exponent prime factors of 12 and 18.
First, we will calculate the prime factors of 12 and 18.
Prime Factorization of 12
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2 12
2 6
3 3
1
Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:
12 = 22×31
Prime Factorization of 18
2 18
3 9
3 3
1
Prime factors of 18 are 2,3. Prime factorization of 18 in exponential form is:
18 = 21×32
Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 18.
LCM(12,18) = 22×32
LCM(12,18) = 36
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Factors of 18
List of positive integer factors of 18 that divides 18 without a remainder.
1, 2, 3, 6, 9, 18
Least Common Multiple of 12 and 18 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate the greatest common factor 12 and 18 then apply to the LCM equation.
GCF(12,18) = 6
LCM(12,18) = ( 12 × 18) / 6
LCM(12,18) = 216 / 6
LCM(12,18) = 36
Least Common Multiple of 12 and 18 by Listing Multiples
Multiples of 12
12, 24,36
Multiples of 18
18,36
Find the smallest number that is on all of the lists. We have it in bold above.
∴ Least Common Multiple of 12 and 18 is 36
Properties of LCM 12 and 18
(i) The LCM of 18 and 12 is associative
LCM of 12 and 18 = LCM of 18 and 12
Frequently Asked Questions on LCM of 12 and 18
1. What is the LCM of 12 and 18?
Answer: LCM of 12 and 18 is 36.
2. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
3. What are the Factors of 18?
Answer: Factors of 18 are 1, 2, 3, 6, 9, 18. There are 6 integers that are factors of 18. The greatest factor of 18 is 18.
4. How to Find the LCM of 12 and 18?
Answer:
Least Common Multiple of 12 and 18 = 36
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 18
18 = 2 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 36 = 2 x 2 x 3 x 3
Step 4: Therefore, the least common multiple of 12 and 18 is 36.