Least Common Multiple of 31 and 35

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

• Least Common Multiple of 31 and 35 by Prime method
• Least Common Multiple of 31 and 35 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 35. First we will calculate the prime factors of 31 and 35.

Prime Factorization of 31

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

31 = 31¹

Prime Factorization of 35

Prime factors of 35 are 5,7. Prime factorization of 35 in exponential form is:

35 = 5¹×7¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 35.

LCM(31,35) = 5¹×7¹×31¹
LCM(31,35) = 1085

Factors of 31

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

1, 31

Factors of 35

List of positive integer factors of 35 that divides 35 without a remainder.

1, 5, 7, 35

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 35, than apply into the LCM equation.

GCF(31,35) = 1
LCM(31,35) = ( 31 × 35) / 1
LCM(31,35) = 1085 / 1
LCM(31,35) = 1085

(i) The LCM of 35 and 31 is associative

LCM of 31 and 35 = LCM of 35 and 31

1. What is the LCM of 31 and 35?

Answer: LCM of 31 and 35 is 1085.

2. 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.

3. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

4. How to Find the LCM of 31 and 35?

Answer:

Least Common Multiple of 31 and 35 = 1085

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 35

35 = 5 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 = 1085 = 5 x 7 x 31

Step 4: Therefore, the least common multiple of 31 and 35 is 1085.