Least Common Multiple of 38 and 46

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 38 and 46 the smallest integer that is 874 that is divisible by both numbers.

Least Common Multiple (LCM) of 38 and 46 is 874.

LCM(38,46) = 874

LCM of 38 and 46

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

LCM of:
and

Least Common Multiple of 38 and 46

LCM of 38 and 46 is 874

Least common multiple can be found by multiplying the highest exponent prime factors of 38 and 46. First we will calculate the prime factors of 38 and 46.

Prime Factorization of 38


2 38
19 19
1

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

38 = 21×191

Prime Factorization of 46


2 46
23 23
1

Prime factors of 46 are 2,23. Prime factorization of 46 in exponential form is:

46 = 21×231

Now multiplying the highest exponent prime factors to calculate the LCM of 38 and 46.

LCM(38,46) = 21×191×231
LCM(38,46) = 874

Factors of 38

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

1, 2, 19, 38

Factors of 46

List of positive integer factors of 46 that divides 46 without a remainder.

1, 2, 23, 46

Least Common Multiple of 38 and 46 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 46, than apply into the LCM equation.

GCF(38,46) = 2
LCM(38,46) = ( 38 × 46) / 2
LCM(38,46) = 1748 / 2
LCM(38,46) = 874

Properties of LCM 38 and 46

(i) The LCM of 46 and 38 is associative

LCM of 38 and 46 = LCM of 46 and 38

Related Least Common Multiples of 38

Related Least Common Multiples of 46

Frequently Asked Questions on LCM of 38 and 46

1. What is the LCM of 38 and 46?

Answer: LCM of 38 and 46 is 874.

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 46?

Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.

4. How to Find the LCM of 38 and 46?

Answer:

Least Common Multiple of 38 and 46 = 874

Step 1: Find the prime factorization of 38

38 = 2 x 19

Step 2: Find the prime factorization of 46

46 = 2 x 23

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

LCM = 874 = 2 x 19 x 23

Step 4: Therefore, the least common multiple of 38 and 46 is 874.