Least Common Multiple of 7 and 18

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 7 and 18 by Prime method
• Least Common Multiple of 7 and 18 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 7 and 18. First we will calculate the prime factors of 7 and 18.

Prime Factorization of 7

Prime factors of 7 are 7. Prime factorization of 7 in exponential form is:

7 = 7¹

Prime Factorization of 18

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 7 and 18.

LCM(7,18) = 2¹×3²×7¹
LCM(7,18) = 126

Factors of 7

List of positive integer factors of 7 that divides 7 without a remainder.

1, 7

Factors of 18

List of positive integer factors of 18 that divides 18 without a remainder.

1, 2, 3, 6, 9, 18

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7 and 18, than apply into the LCM equation.

GCF(7,18) = 1
LCM(7,18) = ( 7 × 18) / 1
LCM(7,18) = 126 / 1
LCM(7,18) = 126

(i) The LCM of 18 and 7 is associative

LCM of 7 and 18 = LCM of 18 and 7

1. What is the LCM of 7 and 18?

Answer: LCM of 7 and 18 is 126.

2. What are the Factors of 7?

Answer: Factors of 7 are 1, 7. There are 2 integers that are factors of 7. The greatest factor of 7 is 7.

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 7 and 18?

Answer:

Least Common Multiple of 7 and 18 = 126

Step 1: Find the prime factorization of 7

7 = 7

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 = 126 = 2 x 3 x 3 x 7

Step 4: Therefore, the least common multiple of 7 and 18 is 126.