Least Common Multiple of 3420 and 3424

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3420 and 3424 the smallest integer that is 2927520 that is divisible by both numbers.

Least Common Multiple (LCM) of 3420 and 3424 is 2927520.

LCM(3420,3424) = 2927520

LCM of 3420 and 3424

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

LCM of:
and

Least Common Multiple of 3420 and 3424

LCM of 3420 and 3424 is 2927520

Least common multiple can be found by multiplying the highest exponent prime factors of 3420 and 3424. First we will calculate the prime factors of 3420 and 3424.

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

Prime Factorization of 3424


2 3424
2 1712
2 856
2 428
2 214
107 107
1

Prime factors of 3424 are 2,107. Prime factorization of 3424 in exponential form is:

3424 = 25×1071

Now multiplying the highest exponent prime factors to calculate the LCM of 3420 and 3424.

LCM(3420,3424) = 25×32×51×191×1071
LCM(3420,3424) = 2927520

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

Factors of 3424

List of positive integer factors of 3424 that divides 3424 without a remainder.

1, 2, 4, 8, 16, 32, 107, 214, 428, 856, 1712, 3424

Least Common Multiple of 3420 and 3424 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3420 and 3424, than apply into the LCM equation.

GCF(3420,3424) = 4
LCM(3420,3424) = ( 3420 × 3424) / 4
LCM(3420,3424) = 11710080 / 4
LCM(3420,3424) = 2927520

Properties of LCM 3420 and 3424

(i) The LCM of 3424 and 3420 is associative

LCM of 3420 and 3424 = LCM of 3424 and 3420

Related Least Common Multiples of 3420

Related Least Common Multiples of 3424

Frequently Asked Questions on LCM of 3420 and 3424

1. What is the LCM of 3420 and 3424?

Answer: LCM of 3420 and 3424 is 2927520.

2. 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.

3. What are the Factors of 3424?

Answer: Factors of 3424 are 1, 2, 4, 8, 16, 32, 107, 214, 428, 856, 1712, 3424. There are 12 integers that are factors of 3424. The greatest factor of 3424 is 3424.

4. How to Find the LCM of 3420 and 3424?

Answer:

Least Common Multiple of 3420 and 3424 = 2927520

Step 1: Find the prime factorization of 3420

3420 = 2 x 2 x 3 x 3 x 5 x 19

Step 2: Find the prime factorization of 3424

3424 = 2 x 2 x 2 x 2 x 2 x 107

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

LCM = 2927520 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 x 19 x 107

Step 4: Therefore, the least common multiple of 3420 and 3424 is 2927520.