Least Common Multiple of 39 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 39 and 46 the smallest integer that is 1794 that is divisible by both numbers.

Least Common Multiple (LCM) of 39 and 46 is 1794.

LCM(39,46) = 1794

LCM of 39 and 46

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

LCM of:
and

Least Common Multiple of 39 and 46

LCM of 39 and 46 is 1794

Least common multiple can be found by multiplying the highest exponent prime factors of 39 and 46. First we will calculate the prime factors of 39 and 46.

Prime Factorization of 39


3 39
13 13
1

Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:

39 = 31×131

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 39 and 46.

LCM(39,46) = 21×31×131×231
LCM(39,46) = 1794

Factors of 39

List of positive integer factors of 39 that divides 39 without a remainder.

1, 3, 13, 39

Factors of 46

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

1, 2, 23, 46

Least Common Multiple of 39 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 39 and 46, than apply into the LCM equation.

GCF(39,46) = 1
LCM(39,46) = ( 39 × 46) / 1
LCM(39,46) = 1794 / 1
LCM(39,46) = 1794

Properties of LCM 39 and 46

(i) The LCM of 46 and 39 is associative

LCM of 39 and 46 = LCM of 46 and 39

Related Least Common Multiples of 39

Related Least Common Multiples of 46

Frequently Asked Questions on LCM of 39 and 46

1. What is the LCM of 39 and 46?

Answer: LCM of 39 and 46 is 1794.

2. What are the Factors of 39?

Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.

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 39 and 46?

Answer:

Least Common Multiple of 39 and 46 = 1794

Step 1: Find the prime factorization of 39

39 = 3 x 13

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 = 1794 = 2 x 3 x 13 x 23

Step 4: Therefore, the least common multiple of 39 and 46 is 1794.