Least Common Multiple of 30 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 30 and 46 the smallest integer that is 690 that is divisible by both numbers.

Least Common Multiple (LCM) of 30 and 46 is 690.

LCM(30,46) = 690

LCM of 30 and 46

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

LCM of:
and

Least Common Multiple of 30 and 46

LCM of 30 and 46 is 690

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 46. First we will calculate the prime factors of 30 and 46.

Prime Factorization of 30


2 30
3 15
5 5
1

Prime factors of 30 are 2, 3,5. Prime factorization of 30 in exponential form is:

30 = 21×31×51

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 30 and 46.

LCM(30,46) = 21×31×51×231
LCM(30,46) = 690

Factors of 30

List of positive integer factors of 30 that divides 30 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30

Factors of 46

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

1, 2, 23, 46

Least Common Multiple of 30 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 30 and 46, than apply into the LCM equation.

GCF(30,46) = 2
LCM(30,46) = ( 30 × 46) / 2
LCM(30,46) = 1380 / 2
LCM(30,46) = 690

Properties of LCM 30 and 46

(i) The LCM of 46 and 30 is associative

LCM of 30 and 46 = LCM of 46 and 30

Related Least Common Multiples of 30

Related Least Common Multiples of 46

Frequently Asked Questions on LCM of 30 and 46

1. What is the LCM of 30 and 46?

Answer: LCM of 30 and 46 is 690.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

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 30 and 46?

Answer:

Least Common Multiple of 30 and 46 = 690

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 = 690 = 2 x 3 x 5 x 23

Step 4: Therefore, the least common multiple of 30 and 46 is 690.