Least Common Multiple of 14 and 33

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 14 and 33 the smallest integer that is 462 that is divisible by both numbers.

Least Common Multiple (LCM) of 14 and 33 is 462.

LCM(14,33) = 462

LCM of 14 and 33

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

LCM of:
and

Least Common Multiple of 14 and 33

LCM of 14 and 33 is 462

Least common multiple can be found by multiplying the highest exponent prime factors of 14 and 33. First we will calculate the prime factors of 14 and 33.

Prime Factorization of 14


2 14
7 7
1

Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:

14 = 21×71

Prime Factorization of 33


3 33
11 11
1

Prime factors of 33 are 3,11. Prime factorization of 33 in exponential form is:

33 = 31×111

Now multiplying the highest exponent prime factors to calculate the LCM of 14 and 33.

LCM(14,33) = 21×31×71×111
LCM(14,33) = 462

Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7, 14

Factors of 33

List of positive integer factors of 33 that divides 33 without a remainder.

1, 3, 11, 33

Least Common Multiple of 14 and 33 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 14 and 33, than apply into the LCM equation.

GCF(14,33) = 1
LCM(14,33) = ( 14 × 33) / 1
LCM(14,33) = 462 / 1
LCM(14,33) = 462

Properties of LCM 14 and 33

(i) The LCM of 33 and 14 is associative

LCM of 14 and 33 = LCM of 33 and 14

Related Least Common Multiples of 14

Related Least Common Multiples of 33

Frequently Asked Questions on LCM of 14 and 33

1. What is the LCM of 14 and 33?

Answer: LCM of 14 and 33 is 462.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

3. What are the Factors of 33?

Answer: Factors of 33 are 1, 3, 11, 33. There are 4 integers that are factors of 33. The greatest factor of 33 is 33.

4. How to Find the LCM of 14 and 33?

Answer:

Least Common Multiple of 14 and 33 = 462

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 33

33 = 3 x 11

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

LCM = 462 = 2 x 3 x 7 x 11

Step 4: Therefore, the least common multiple of 14 and 33 is 462.