Least Common Multiple of 7034 and 7038

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 7034 and 7038 the smallest integer that is 24752646 that is divisible by both numbers.

Least Common Multiple (LCM) of 7034 and 7038 is 24752646.

LCM(7034,7038) = 24752646

LCM of 7034 and 7038

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

LCM of:
and

Least Common Multiple of 7034 and 7038

LCM of 7034 and 7038 is 24752646

Least common multiple can be found by multiplying the highest exponent prime factors of 7034 and 7038. First we will calculate the prime factors of 7034 and 7038.

Prime Factorization of 7034


2 7034
3517 3517
1

Prime factors of 7034 are 2,3517. Prime factorization of 7034 in exponential form is:

7034 = 21×35171

Prime Factorization of 7038


2 7038
3 3519
3 1173
17 391
23 23
1

Prime factors of 7038 are 2, 3, 17,23. Prime factorization of 7038 in exponential form is:

7038 = 21×32×171×231

Now multiplying the highest exponent prime factors to calculate the LCM of 7034 and 7038.

LCM(7034,7038) = 21×32×171×231×35171
LCM(7034,7038) = 24752646

Factors of 7034

List of positive integer factors of 7034 that divides 7034 without a remainder.

1, 2, 3517, 7034

Factors of 7038

List of positive integer factors of 7038 that divides 7038 without a remainder.

1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519, 7038

Least Common Multiple of 7034 and 7038 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7034 and 7038, than apply into the LCM equation.

GCF(7034,7038) = 2
LCM(7034,7038) = ( 7034 × 7038) / 2
LCM(7034,7038) = 49505292 / 2
LCM(7034,7038) = 24752646

Properties of LCM 7034 and 7038

(i) The LCM of 7038 and 7034 is associative

LCM of 7034 and 7038 = LCM of 7038 and 7034

Related Least Common Multiples of 7034

Related Least Common Multiples of 7038

Frequently Asked Questions on LCM of 7034 and 7038

1. What is the LCM of 7034 and 7038?

Answer: LCM of 7034 and 7038 is 24752646.

2. What are the Factors of 7034?

Answer: Factors of 7034 are 1, 2, 3517, 7034. There are 4 integers that are factors of 7034. The greatest factor of 7034 is 7034.

3. What are the Factors of 7038?

Answer: Factors of 7038 are 1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519, 7038. There are 24 integers that are factors of 7038. The greatest factor of 7038 is 7038.

4. How to Find the LCM of 7034 and 7038?

Answer:

Least Common Multiple of 7034 and 7038 = 24752646

Step 1: Find the prime factorization of 7034

7034 = 2 x 3517

Step 2: Find the prime factorization of 7038

7038 = 2 x 3 x 3 x 17 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 = 24752646 = 2 x 3 x 3 x 17 x 23 x 3517

Step 4: Therefore, the least common multiple of 7034 and 7038 is 24752646.