Least Common Multiple of 2 and 5

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

• Least Common Multiple of 2 and 5 by Prime method
• Least Common Multiple of 2 and 5 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 2 and 5. First we will calculate the prime factors of 2 and 5.

Prime Factorization of 2

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

2 = 2¹

Prime Factorization of 5

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

5 = 5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 2 and 5.

LCM(2,5) = 2¹×5¹
LCM(2,5) = 10

Factors of 2

List of positive integer factors of 2 that divides 2 without a remainder.

1, 2

Factors of 5

List of positive integer factors of 5 that divides 5 without a remainder.

1, 5

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2 and 5, than apply into the LCM equation.

GCF(2,5) = 1
LCM(2,5) = ( 2 × 5) / 1
LCM(2,5) = 10 / 1
LCM(2,5) = 10

(i) The LCM of 5 and 2 is associative

LCM of 2 and 5 = LCM of 5 and 2

1. What is the LCM of 2 and 5?

Answer: LCM of 2 and 5 is 10.

2. What are the Factors of 2?

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

3. What are the Factors of 5?

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

4. How to Find the LCM of 2 and 5?

Answer:

Least Common Multiple of 2 and 5 = 10

Step 1: Find the prime factorization of 2

2 = 2

Step 2: Find the prime factorization of 5

5 = 5

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

LCM = 10 = 2 x 5

Step 4: Therefore, the least common multiple of 2 and 5 is 10.