Least Common Multiple of 3412 and 3420

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3412 and 3420 the smallest integer that is 2917260 that is divisible by both numbers.

Least Common Multiple (LCM) of 3412 and 3420 is 2917260.

LCM(3412,3420) = 2917260

LCM of 3412 and 3420

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

LCM of:
and

Least Common Multiple of 3412 and 3420

LCM of 3412 and 3420 is 2917260

Least common multiple can be found by multiplying the highest exponent prime factors of 3412 and 3420. First we will calculate the prime factors of 3412 and 3420.

Prime Factorization of 3412


2 3412
2 1706
853 853
1

Prime factors of 3412 are 2,853. Prime factorization of 3412 in exponential form is:

3412 = 22×8531

Prime Factorization of 3420


2 3420
2 1710
3 855
3 285
5 95
19 19
1

Prime factors of 3420 are 2, 3, 5,19. Prime factorization of 3420 in exponential form is:

3420 = 22×32×51×191

Now multiplying the highest exponent prime factors to calculate the LCM of 3412 and 3420.

LCM(3412,3420) = 22×32×51×191×8531
LCM(3412,3420) = 2917260

Factors of 3412

List of positive integer factors of 3412 that divides 3412 without a remainder.

1, 2, 4, 853, 1706, 3412

Factors of 3420

List of positive integer factors of 3420 that divides 3420 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 380, 570, 684, 855, 1140, 1710, 3420

Least Common Multiple of 3412 and 3420 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3412 and 3420, than apply into the LCM equation.

GCF(3412,3420) = 4
LCM(3412,3420) = ( 3412 × 3420) / 4
LCM(3412,3420) = 11669040 / 4
LCM(3412,3420) = 2917260

Properties of LCM 3412 and 3420

(i) The LCM of 3420 and 3412 is associative

LCM of 3412 and 3420 = LCM of 3420 and 3412

Related Least Common Multiples of 3412

Related Least Common Multiples of 3420

Frequently Asked Questions on LCM of 3412 and 3420

1. What is the LCM of 3412 and 3420?

Answer: LCM of 3412 and 3420 is 2917260.

2. What are the Factors of 3412?

Answer: Factors of 3412 are 1, 2, 4, 853, 1706, 3412. There are 6 integers that are factors of 3412. The greatest factor of 3412 is 3412.

3. What are the Factors of 3420?

Answer: Factors of 3420 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 380, 570, 684, 855, 1140, 1710, 3420. There are 36 integers that are factors of 3420. The greatest factor of 3420 is 3420.

4. How to Find the LCM of 3412 and 3420?

Answer:

Least Common Multiple of 3412 and 3420 = 2917260

Step 1: Find the prime factorization of 3412

3412 = 2 x 2 x 853

Step 2: Find the prime factorization of 3420

3420 = 2 x 2 x 3 x 3 x 5 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 = 2917260 = 2 x 2 x 3 x 3 x 5 x 19 x 853

Step 4: Therefore, the least common multiple of 3412 and 3420 is 2917260.