Least Common Multiple of 2123 and 2128

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2123 and 2128 the smallest integer that is 4517744 that is divisible by both numbers.

Least Common Multiple (LCM) of 2123 and 2128 is 4517744.

LCM(2123,2128) = 4517744

LCM of 2123 and 2128

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

LCM of:
and

Least Common Multiple of 2123 and 2128

LCM of 2123 and 2128 is 4517744

Least common multiple can be found by multiplying the highest exponent prime factors of 2123 and 2128. First we will calculate the prime factors of 2123 and 2128.

Prime Factorization of 2123


11 2123
193 193
1

Prime factors of 2123 are 11,193. Prime factorization of 2123 in exponential form is:

2123 = 111×1931

Prime Factorization of 2128


2 2128
2 1064
2 532
2 266
7 133
19 19
1

Prime factors of 2128 are 2, 7,19. Prime factorization of 2128 in exponential form is:

2128 = 24×71×191

Now multiplying the highest exponent prime factors to calculate the LCM of 2123 and 2128.

LCM(2123,2128) = 24×71×111×191×1931
LCM(2123,2128) = 4517744

Factors of 2123

List of positive integer factors of 2123 that divides 2123 without a remainder.

1, 11, 193, 2123

Factors of 2128

List of positive integer factors of 2128 that divides 2128 without a remainder.

1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 56, 76, 112, 133, 152, 266, 304, 532, 1064, 2128

Least Common Multiple of 2123 and 2128 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2123 and 2128, than apply into the LCM equation.

GCF(2123,2128) = 1
LCM(2123,2128) = ( 2123 × 2128) / 1
LCM(2123,2128) = 4517744 / 1
LCM(2123,2128) = 4517744

Properties of LCM 2123 and 2128

(i) The LCM of 2128 and 2123 is associative

LCM of 2123 and 2128 = LCM of 2128 and 2123

Related Least Common Multiples of 2123

Related Least Common Multiples of 2128

Frequently Asked Questions on LCM of 2123 and 2128

1. What is the LCM of 2123 and 2128?

Answer: LCM of 2123 and 2128 is 4517744.

2. What are the Factors of 2123?

Answer: Factors of 2123 are 1, 11, 193, 2123. There are 4 integers that are factors of 2123. The greatest factor of 2123 is 2123.

3. What are the Factors of 2128?

Answer: Factors of 2128 are 1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 56, 76, 112, 133, 152, 266, 304, 532, 1064, 2128. There are 20 integers that are factors of 2128. The greatest factor of 2128 is 2128.

4. How to Find the LCM of 2123 and 2128?

Answer:

Least Common Multiple of 2123 and 2128 = 4517744

Step 1: Find the prime factorization of 2123

2123 = 11 x 193

Step 2: Find the prime factorization of 2128

2128 = 2 x 2 x 2 x 2 x 7 x 19

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

LCM = 4517744 = 2 x 2 x 2 x 2 x 7 x 11 x 19 x 193

Step 4: Therefore, the least common multiple of 2123 and 2128 is 4517744.