Least Common Multiple of 38 and 43

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

• Least Common Multiple of 38 and 43 by Prime method
• Least Common Multiple of 38 and 43 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 38 and 43. First we will calculate the prime factors of 38 and 43.

Prime Factorization of 38

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

38 = 2¹×19¹

Prime Factorization of 43

Prime factors of 43 are 43. Prime factorization of 43 in exponential form is:

43 = 43¹

Now multiplying the highest exponent prime factors to calculate the LCM of 38 and 43.

LCM(38,43) = 2¹×19¹×43¹
LCM(38,43) = 1634

Factors of 38

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

1, 2, 19, 38

Factors of 43

List of positive integer factors of 43 that divides 43 without a remainder.

1, 43

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 43, than apply into the LCM equation.

GCF(38,43) = 1
LCM(38,43) = ( 38 × 43) / 1
LCM(38,43) = 1634 / 1
LCM(38,43) = 1634

(i) The LCM of 43 and 38 is associative

LCM of 38 and 43 = LCM of 43 and 38

1. What is the LCM of 38 and 43?

Answer: LCM of 38 and 43 is 1634.

2. 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.

3. What are the Factors of 43?

Answer: Factors of 43 are 1, 43. There are 2 integers that are factors of 43. The greatest factor of 43 is 43.

4. How to Find the LCM of 38 and 43?

Answer:

Least Common Multiple of 38 and 43 = 1634

Step 1: Find the prime factorization of 38

38 = 2 x 19

Step 2: Find the prime factorization of 43

43 = 43

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

LCM = 1634 = 2 x 19 x 43

Step 4: Therefore, the least common multiple of 38 and 43 is 1634.