Least Common Multiple of 3400 and 3402

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 3400 and 3402 the smallest integer that is 5783400 that is divisible by both numbers.

Least Common Multiple (LCM) of 3400 and 3402 is 5783400.

LCM(3400,3402) = 5783400

LCM of 3400 and 3402

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

LCM of:
and

Least Common Multiple of 3400 and 3402

LCM of 3400 and 3402 is 5783400

Least common multiple can be found by multiplying the highest exponent prime factors of 3400 and 3402. First we will calculate the prime factors of 3400 and 3402.

Prime Factorization of 3400


2 3400
2 1700
2 850
5 425
5 85
17 17
1

Prime factors of 3400 are 2, 5,17. Prime factorization of 3400 in exponential form is:

3400 = 23×52×171

Prime Factorization of 3402


2 3402
3 1701
3 567
3 189
3 63
3 21
7 7
1

Prime factors of 3402 are 2, 3,7. Prime factorization of 3402 in exponential form is:

3402 = 21×35×71

Now multiplying the highest exponent prime factors to calculate the LCM of 3400 and 3402.

LCM(3400,3402) = 23×35×52×71×171
LCM(3400,3402) = 5783400

Factors of 3400

List of positive integer factors of 3400 that divides 3400 without a remainder.

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400

Factors of 3402

List of positive integer factors of 3402 that divides 3402 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402

Least Common Multiple of 3400 and 3402 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3400 and 3402, than apply into the LCM equation.

GCF(3400,3402) = 2
LCM(3400,3402) = ( 3400 × 3402) / 2
LCM(3400,3402) = 11566800 / 2
LCM(3400,3402) = 5783400

Properties of LCM 3400 and 3402

(i) The LCM of 3402 and 3400 is associative

LCM of 3400 and 3402 = LCM of 3402 and 3400

Related Least Common Multiples of 3400

Related Least Common Multiples of 3402

Frequently Asked Questions on LCM of 3400 and 3402

1. What is the LCM of 3400 and 3402?

Answer: LCM of 3400 and 3402 is 5783400.

2. What are the Factors of 3400?

Answer: Factors of 3400 are 1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400. There are 24 integers that are factors of 3400. The greatest factor of 3400 is 3400.

3. What are the Factors of 3402?

Answer: Factors of 3402 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 81, 126, 162, 189, 243, 378, 486, 567, 1134, 1701, 3402. There are 24 integers that are factors of 3402. The greatest factor of 3402 is 3402.

4. How to Find the LCM of 3400 and 3402?

Answer:

Least Common Multiple of 3400 and 3402 = 5783400

Step 1: Find the prime factorization of 3400

3400 = 2 x 2 x 2 x 5 x 5 x 17

Step 2: Find the prime factorization of 3402

3402 = 2 x 3 x 3 x 3 x 3 x 3 x 7

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

LCM = 5783400 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 7 x 17

Step 4: Therefore, the least common multiple of 3400 and 3402 is 5783400.