Least Common Multiple of 9 and 16

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 9 and 16 the smallest integer that is 144 that is divisible by both numbers.

Least Common Multiple (LCM) of 9 and 16 is 144.

LCM(9,16) = 144

LCM of 9 and 16

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

LCM of:
and

Least Common Multiple of 9 and 16

LCM of 9 and 16 is 144

Least common multiple can be found by multiplying the highest exponent prime factors of 9 and 16. First we will calculate the prime factors of 9 and 16.

Prime Factorization of 9


3 9
3 3
1

Prime factors of 9 are 3. Prime factorization of 9 in exponential form is:

9 = 32

Prime Factorization of 16


2 16
2 8
2 4
2 2
1

Prime factors of 16 are 2. Prime factorization of 16 in exponential form is:

16 = 24

Now multiplying the highest exponent prime factors to calculate the LCM of 9 and 16.

LCM(9,16) = 24×32
LCM(9,16) = 144

Factors of 9

List of positive integer factors of 9 that divides 9 without a remainder.

1, 3, 9

Factors of 16

List of positive integer factors of 16 that divides 16 without a remainder.

1, 2, 4, 8, 16

Least Common Multiple of 9 and 16 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9 and 16, than apply into the LCM equation.

GCF(9,16) = 1
LCM(9,16) = ( 9 × 16) / 1
LCM(9,16) = 144 / 1
LCM(9,16) = 144

Properties of LCM 9 and 16

(i) The LCM of 16 and 9 is associative

LCM of 9 and 16 = LCM of 16 and 9

Related Least Common Multiples of 9

Related Least Common Multiples of 16

Frequently Asked Questions on LCM of 9 and 16

1. What is the LCM of 9 and 16?

Answer: LCM of 9 and 16 is 144.

2. What are the Factors of 9?

Answer: Factors of 9 are 1, 3, 9. There are 3 integers that are factors of 9. The greatest factor of 9 is 9.

3. What are the Factors of 16?

Answer: Factors of 16 are 1, 2, 4, 8, 16. There are 5 integers that are factors of 16. The greatest factor of 16 is 16.

4. How to Find the LCM of 9 and 16?

Answer:

Least Common Multiple of 9 and 16 = 144

Step 1: Find the prime factorization of 9

9 = 3 x 3

Step 2: Find the prime factorization of 16

16 = 2 x 2 x 2 x 2

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

LCM = 144 = 2 x 2 x 2 x 2 x 3 x 3

Step 4: Therefore, the least common multiple of 9 and 16 is 144.