Least Common Multiple of 3456 and 3462

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3456 and 3462 the smallest integer that is 1994112 that is divisible by both numbers.

Least Common Multiple (LCM) of 3456 and 3462 is 1994112.

LCM(3456,3462) = 1994112

LCM of 3456 and 3462

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

LCM of:
and

Least Common Multiple of 3456 and 3462

LCM of 3456 and 3462 is 1994112

Least common multiple can be found by multiplying the highest exponent prime factors of 3456 and 3462. First we will calculate the prime factors of 3456 and 3462.

Prime Factorization of 3456


2 3456
2 1728
2 864
2 432
2 216
2 108
2 54
3 27
3 9
3 3
1

Prime factors of 3456 are 2,3. Prime factorization of 3456 in exponential form is:

3456 = 27×33

Prime Factorization of 3462


2 3462
3 1731
577 577
1

Prime factors of 3462 are 2, 3,577. Prime factorization of 3462 in exponential form is:

3462 = 21×31×5771

Now multiplying the highest exponent prime factors to calculate the LCM of 3456 and 3462.

LCM(3456,3462) = 27×33×5771
LCM(3456,3462) = 1994112

Factors of 3456

List of positive integer factors of 3456 that divides 3456 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 288, 384, 432, 576, 864, 1152, 1728, 3456

Factors of 3462

List of positive integer factors of 3462 that divides 3462 without a remainder.

1, 2, 3, 6, 577, 1154, 1731, 3462

Least Common Multiple of 3456 and 3462 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3456 and 3462, than apply into the LCM equation.

GCF(3456,3462) = 6
LCM(3456,3462) = ( 3456 × 3462) / 6
LCM(3456,3462) = 11964672 / 6
LCM(3456,3462) = 1994112

Properties of LCM 3456 and 3462

(i) The LCM of 3462 and 3456 is associative

LCM of 3456 and 3462 = LCM of 3462 and 3456

Related Least Common Multiples of 3456

Related Least Common Multiples of 3462

Frequently Asked Questions on LCM of 3456 and 3462

1. What is the LCM of 3456 and 3462?

Answer: LCM of 3456 and 3462 is 1994112.

2. What are the Factors of 3456?

Answer: Factors of 3456 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 128, 144, 192, 216, 288, 384, 432, 576, 864, 1152, 1728, 3456. There are 32 integers that are factors of 3456. The greatest factor of 3456 is 3456.

3. What are the Factors of 3462?

Answer: Factors of 3462 are 1, 2, 3, 6, 577, 1154, 1731, 3462. There are 8 integers that are factors of 3462. The greatest factor of 3462 is 3462.

4. How to Find the LCM of 3456 and 3462?

Answer:

Least Common Multiple of 3456 and 3462 = 1994112

Step 1: Find the prime factorization of 3456

3456 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 3462

3462 = 2 x 3 x 577

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

LCM = 1994112 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 577

Step 4: Therefore, the least common multiple of 3456 and 3462 is 1994112.