Least Common Multiple of 15 and 31

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

• Least Common Multiple of 15 and 31 by Prime method
• Least Common Multiple of 15 and 31 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 31. First we will calculate the prime factors of 15 and 31.

Prime Factorization of 15

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

15 = 3¹×5¹

Prime Factorization of 31

Prime factors of 31 are 31. Prime factorization of 31 in exponential form is:

31 = 31¹

Now multiplying the highest exponent prime factors to calculate the LCM of 15 and 31.

LCM(15,31) = 3¹×5¹×31¹
LCM(15,31) = 465

Factors of 15

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

1, 3, 5, 15

Factors of 31

List of positive integer factors of 31 that divides 31 without a remainder.

1, 31

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 15 and 31, than apply into the LCM equation.

GCF(15,31) = 1
LCM(15,31) = ( 15 × 31) / 1
LCM(15,31) = 465 / 1
LCM(15,31) = 465

(i) The LCM of 31 and 15 is associative

LCM of 15 and 31 = LCM of 31 and 15

1. What is the LCM of 15 and 31?

Answer: LCM of 15 and 31 is 465.

2. 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.

3. What are the Factors of 31?

Answer: Factors of 31 are 1, 31. There are 2 integers that are factors of 31. The greatest factor of 31 is 31.

4. How to Find the LCM of 15 and 31?

Answer:

Least Common Multiple of 15 and 31 = 465

Step 1: Find the prime factorization of 15

15 = 3 x 5

Step 2: Find the prime factorization of 31

31 = 31

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

LCM = 465 = 3 x 5 x 31

Step 4: Therefore, the least common multiple of 15 and 31 is 465.