Least Common Multiple of 14 and 15

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

• Least Common Multiple of 14 and 15 by Prime method
• Least Common Multiple of 14 and 15 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 15. First we will calculate the prime factors of 14 and 15.

Prime Factorization of 14

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 2¹×7¹

Prime Factorization of 15

Prime factors of 15 are 3,5. Prime factorization of 15 in exponential form is:

15 = 3¹×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 15.

LCM(14,15) = 2¹×3¹×5¹×7¹
LCM(14,15) = 210

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

Factors of 15

List of positive integer factors of 15 that divides 15 without a remainder.

1, 3, 5, 15

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 15, than apply into the LCM equation.

GCF(14,15) = 1
LCM(14,15) = ( 14 × 15) / 1
LCM(14,15) = 210 / 1
LCM(14,15) = 210

(i) The LCM of 15 and 14 is associative

LCM of 14 and 15 = LCM of 15 and 14

1. What is the LCM of 14 and 15?

Answer: LCM of 14 and 15 is 210.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

3. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

4. How to Find the LCM of 14 and 15?

Answer:

Least Common Multiple of 14 and 15 = 210

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 15

15 = 3 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 210 = 2 x 3 x 5 x 7

Step 4: Therefore, the least common multiple of 14 and 15 is 210.