Least Common Multiple of 31 and 34

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

• Least Common Multiple of 31 and 34 by Prime method
• Least Common Multiple of 31 and 34 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 31 and 34. First we will calculate the prime factors of 31 and 34.

Prime Factorization of 31

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

31 = 31¹

Prime Factorization of 34

Prime factors of 34 are 2,17. Prime factorization of 34 in exponential form is:

34 = 2¹×17¹

Now multiplying the highest exponent prime factors to calculate the LCM of 31 and 34.

LCM(31,34) = 2¹×17¹×31¹
LCM(31,34) = 1054

Factors of 31

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

1, 31

Factors of 34

List of positive integer factors of 34 that divides 34 without a remainder.

1, 2, 17, 34

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31 and 34, than apply into the LCM equation.

GCF(31,34) = 1
LCM(31,34) = ( 31 × 34) / 1
LCM(31,34) = 1054 / 1
LCM(31,34) = 1054

(i) The LCM of 34 and 31 is associative

LCM of 31 and 34 = LCM of 34 and 31

1. What is the LCM of 31 and 34?

Answer: LCM of 31 and 34 is 1054.

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 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

4. How to Find the LCM of 31 and 34?

Answer:

Least Common Multiple of 31 and 34 = 1054

Step 1: Find the prime factorization of 31

31 = 31

Step 2: Find the prime factorization of 34

34 = 2 x 17

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

LCM = 1054 = 2 x 17 x 31

Step 4: Therefore, the least common multiple of 31 and 34 is 1054.