Least Common Multiple of 3450 and 3456

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3450 and 3456 the smallest integer that is 1987200 that is divisible by both numbers.

Least Common Multiple (LCM) of 3450 and 3456 is 1987200.

LCM(3450,3456) = 1987200

LCM of 3450 and 3456

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

LCM of:
and

Least Common Multiple of 3450 and 3456

LCM of 3450 and 3456 is 1987200

Least common multiple can be found by multiplying the highest exponent prime factors of 3450 and 3456. First we will calculate the prime factors of 3450 and 3456.

Prime Factorization of 3450


2 3450
3 1725
5 575
5 115
23 23
1

Prime factors of 3450 are 2, 3, 5,23. Prime factorization of 3450 in exponential form is:

3450 = 21×31×52×231

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

Now multiplying the highest exponent prime factors to calculate the LCM of 3450 and 3456.

LCM(3450,3456) = 27×33×52×231
LCM(3450,3456) = 1987200

Factors of 3450

List of positive integer factors of 3450 that divides 3450 without a remainder.

1, 2, 3, 5, 6, 10, 15, 23, 25, 30, 46, 50, 69, 75, 115, 138, 150, 230, 345, 575, 690, 1150, 1725, 3450

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

Least Common Multiple of 3450 and 3456 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3450 and 3456, than apply into the LCM equation.

GCF(3450,3456) = 6
LCM(3450,3456) = ( 3450 × 3456) / 6
LCM(3450,3456) = 11923200 / 6
LCM(3450,3456) = 1987200

Properties of LCM 3450 and 3456

(i) The LCM of 3456 and 3450 is associative

LCM of 3450 and 3456 = LCM of 3456 and 3450

Related Least Common Multiples of 3450

Related Least Common Multiples of 3456

Frequently Asked Questions on LCM of 3450 and 3456

1. What is the LCM of 3450 and 3456?

Answer: LCM of 3450 and 3456 is 1987200.

2. What are the Factors of 3450?

Answer: Factors of 3450 are 1, 2, 3, 5, 6, 10, 15, 23, 25, 30, 46, 50, 69, 75, 115, 138, 150, 230, 345, 575, 690, 1150, 1725, 3450. There are 24 integers that are factors of 3450. The greatest factor of 3450 is 3450.

3. 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.

4. How to Find the LCM of 3450 and 3456?

Answer:

Least Common Multiple of 3450 and 3456 = 1987200

Step 1: Find the prime factorization of 3450

3450 = 2 x 3 x 5 x 5 x 23

Step 2: 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 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 1987200 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 23

Step 4: Therefore, the least common multiple of 3450 and 3456 is 1987200.