Least Common Multiple of 2345 and 2352

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 2345 and 2352 the smallest integer that is 787920 that is divisible by both numbers.

Least Common Multiple (LCM) of 2345 and 2352 is 787920.

LCM(2345,2352) = 787920

LCM of 2345 and 2352

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

LCM of:
and

Least Common Multiple of 2345 and 2352

LCM of 2345 and 2352 is 787920

Least common multiple can be found by multiplying the highest exponent prime factors of 2345 and 2352. First we will calculate the prime factors of 2345 and 2352.

Prime Factorization of 2345


5 2345
7 469
67 67
1

Prime factors of 2345 are 5, 7,67. Prime factorization of 2345 in exponential form is:

2345 = 51×71×671

Prime Factorization of 2352


2 2352
2 1176
2 588
2 294
3 147
7 49
7 7
1

Prime factors of 2352 are 2, 3,7. Prime factorization of 2352 in exponential form is:

2352 = 24×31×72

Now multiplying the highest exponent prime factors to calculate the LCM of 2345 and 2352.

LCM(2345,2352) = 24×31×51×72×671
LCM(2345,2352) = 787920

Factors of 2345

List of positive integer factors of 2345 that divides 2345 without a remainder.

1, 5, 7, 35, 67, 335, 469, 2345

Factors of 2352

List of positive integer factors of 2352 that divides 2352 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352

Least Common Multiple of 2345 and 2352 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2345 and 2352, than apply into the LCM equation.

GCF(2345,2352) = 7
LCM(2345,2352) = ( 2345 × 2352) / 7
LCM(2345,2352) = 5515440 / 7
LCM(2345,2352) = 787920

Properties of LCM 2345 and 2352

(i) The LCM of 2352 and 2345 is associative

LCM of 2345 and 2352 = LCM of 2352 and 2345

Related Least Common Multiples of 2345

Related Least Common Multiples of 2352

Frequently Asked Questions on LCM of 2345 and 2352

1. What is the LCM of 2345 and 2352?

Answer: LCM of 2345 and 2352 is 787920.

2. What are the Factors of 2345?

Answer: Factors of 2345 are 1, 5, 7, 35, 67, 335, 469, 2345. There are 8 integers that are factors of 2345. The greatest factor of 2345 is 2345.

3. What are the Factors of 2352?

Answer: Factors of 2352 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 42, 48, 49, 56, 84, 98, 112, 147, 168, 196, 294, 336, 392, 588, 784, 1176, 2352. There are 30 integers that are factors of 2352. The greatest factor of 2352 is 2352.

4. How to Find the LCM of 2345 and 2352?

Answer:

Least Common Multiple of 2345 and 2352 = 787920

Step 1: Find the prime factorization of 2345

2345 = 5 x 7 x 67

Step 2: Find the prime factorization of 2352

2352 = 2 x 2 x 2 x 2 x 3 x 7 x 7

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

LCM = 787920 = 2 x 2 x 2 x 2 x 3 x 5 x 7 x 7 x 67

Step 4: Therefore, the least common multiple of 2345 and 2352 is 787920.