Least Common Multiple of 3 and 10

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

• Least Common Multiple of 3 and 10 by Prime method
• Least Common Multiple of 3 and 10 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 10. First we will calculate the prime factors of 3 and 10.

Prime Factorization of 3

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

3 = 3¹

Prime Factorization of 10

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

10 = 2¹×5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 10.

LCM(3,10) = 2¹×3¹×5¹
LCM(3,10) = 30

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

Factors of 10

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

1, 2, 5, 10

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 10, than apply into the LCM equation.

GCF(3,10) = 1
LCM(3,10) = ( 3 × 10) / 1
LCM(3,10) = 30 / 1
LCM(3,10) = 30

(i) The LCM of 10 and 3 is associative

LCM of 3 and 10 = LCM of 10 and 3

1. What is the LCM of 3 and 10?

Answer: LCM of 3 and 10 is 30.

2. What are the Factors of 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

3. 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.

4. How to Find the LCM of 3 and 10?

Answer:

Least Common Multiple of 3 and 10 = 30

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 10

10 = 2 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 = 30 = 2 x 3 x 5

Step 4: Therefore, the least common multiple of 3 and 10 is 30.