Least Common Multiple of 10 and 14

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

• Least Common Multiple of 10 and 14 by Prime method
• Least Common Multiple of 10 and 14 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 14. First we will calculate the prime factors of 10 and 14.

Prime Factorization of 10

Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:

10 = 2¹×5¹

Prime Factorization of 14

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

14 = 2¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 14.

LCM(10,14) = 2¹×5¹×7¹
LCM(10,14) = 70

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Factors of 14

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

1, 2, 7, 14

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 14, than apply into the LCM equation.

GCF(10,14) = 2
LCM(10,14) = ( 10 × 14) / 2
LCM(10,14) = 140 / 2
LCM(10,14) = 70

(i) The LCM of 14 and 10 is associative

LCM of 10 and 14 = LCM of 14 and 10

1. What is the LCM of 10 and 14?

Answer: LCM of 10 and 14 is 70.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

3. 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.

4. How to Find the LCM of 10 and 14?

Answer:

Least Common Multiple of 10 and 14 = 70

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 14

14 = 2 x 7

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

LCM = 70 = 2 x 5 x 7

Step 4: Therefore, the least common multiple of 10 and 14 is 70.