Least Common Multiple of 34 and 37

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

• Least Common Multiple of 34 and 37 by Prime method
• Least Common Multiple of 34 and 37 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 34 and 37. First we will calculate the prime factors of 34 and 37.

Prime Factorization of 34

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

34 = 2¹×17¹

Prime Factorization of 37

Prime factors of 37 are 37. Prime factorization of 37 in exponential form is:

37 = 37¹

Now multiplying the highest exponent prime factors to calculate the LCM of 34 and 37.

LCM(34,37) = 2¹×17¹×37¹
LCM(34,37) = 1258

Factors of 34

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

1, 2, 17, 34

Factors of 37

List of positive integer factors of 37 that divides 37 without a remainder.

1, 37

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 34 and 37, than apply into the LCM equation.

GCF(34,37) = 1
LCM(34,37) = ( 34 × 37) / 1
LCM(34,37) = 1258 / 1
LCM(34,37) = 1258

(i) The LCM of 37 and 34 is associative

LCM of 34 and 37 = LCM of 37 and 34

1. What is the LCM of 34 and 37?

Answer: LCM of 34 and 37 is 1258.

2. 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.

3. What are the Factors of 37?

Answer: Factors of 37 are 1, 37. There are 2 integers that are factors of 37. The greatest factor of 37 is 37.

4. How to Find the LCM of 34 and 37?

Answer:

Least Common Multiple of 34 and 37 = 1258

Step 1: Find the prime factorization of 34

34 = 2 x 17

Step 2: Find the prime factorization of 37

37 = 37

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

LCM = 1258 = 2 x 17 x 37

Step 4: Therefore, the least common multiple of 34 and 37 is 1258.