Least Common Multiple of 37 and 38

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

• Least Common Multiple of 37 and 38 by Prime method
• Least Common Multiple of 37 and 38 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 37 and 38. First we will calculate the prime factors of 37 and 38.

Prime Factorization of 37

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

37 = 37¹

Prime Factorization of 38

Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:

38 = 2¹×19¹

Now multiplying the highest exponent prime factors to calculate the LCM of 37 and 38.

LCM(37,38) = 2¹×19¹×37¹
LCM(37,38) = 1406

Factors of 37

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

1, 37

Factors of 38

List of positive integer factors of 38 that divides 38 without a remainder.

1, 2, 19, 38

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37 and 38, than apply into the LCM equation.

GCF(37,38) = 1
LCM(37,38) = ( 37 × 38) / 1
LCM(37,38) = 1406 / 1
LCM(37,38) = 1406

(i) The LCM of 38 and 37 is associative

LCM of 37 and 38 = LCM of 38 and 37

1. What is the LCM of 37 and 38?

Answer: LCM of 37 and 38 is 1406.

2. 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.

3. What are the Factors of 38?

Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.

4. How to Find the LCM of 37 and 38?

Answer:

Least Common Multiple of 37 and 38 = 1406

Step 1: Find the prime factorization of 37

37 = 37

Step 2: Find the prime factorization of 38

38 = 2 x 19

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

LCM = 1406 = 2 x 19 x 37

Step 4: Therefore, the least common multiple of 37 and 38 is 1406.