Least Common Multiple of 16409 and 16416

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 16409 and 16416 the smallest integer that is 269370144 that is divisible by both numbers.

Least Common Multiple (LCM) of 16409 and 16416 is 269370144.

LCM(16409,16416) = 269370144

LCM of 16409 and 16416

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

LCM of:
and

Least Common Multiple of 16409 and 16416

LCM of 16409 and 16416 is 269370144

Least common multiple can be found by multiplying the highest exponent prime factors of 16409 and 16416. First we will calculate the prime factors of 16409 and 16416.

Prime Factorization of 16409


61 16409
269 269
1

Prime factors of 16409 are 61,269. Prime factorization of 16409 in exponential form is:

16409 = 611×2691

Prime Factorization of 16416


2 16416
2 8208
2 4104
2 2052
2 1026
3 513
3 171
3 57
19 19
1

Prime factors of 16416 are 2, 3,19. Prime factorization of 16416 in exponential form is:

16416 = 25×33×191

Now multiplying the highest exponent prime factors to calculate the LCM of 16409 and 16416.

LCM(16409,16416) = 25×33×191×611×2691
LCM(16409,16416) = 269370144

Factors of 16409

List of positive integer factors of 16409 that divides 16409 without a remainder.

1, 61, 269, 16409

Factors of 16416

List of positive integer factors of 16416 that divides 16416 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 72, 76, 96, 108, 114, 144, 152, 171, 216, 228, 288, 304, 342, 432, 456, 513, 608, 684, 864, 912, 1026, 1368, 1824, 2052, 2736, 4104, 5472, 8208, 16416

Least Common Multiple of 16409 and 16416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 16409 and 16416, than apply into the LCM equation.

GCF(16409,16416) = 1
LCM(16409,16416) = ( 16409 × 16416) / 1
LCM(16409,16416) = 269370144 / 1
LCM(16409,16416) = 269370144

Properties of LCM 16409 and 16416

(i) The LCM of 16416 and 16409 is associative

LCM of 16409 and 16416 = LCM of 16416 and 16409

Related Least Common Multiples of 16409

Related Least Common Multiples of 16416

Frequently Asked Questions on LCM of 16409 and 16416

1. What is the LCM of 16409 and 16416?

Answer: LCM of 16409 and 16416 is 269370144.

2. What are the Factors of 16409?

Answer: Factors of 16409 are 1, 61, 269, 16409. There are 4 integers that are factors of 16409. The greatest factor of 16409 is 16409.

3. What are the Factors of 16416?

Answer: Factors of 16416 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 19, 24, 27, 32, 36, 38, 48, 54, 57, 72, 76, 96, 108, 114, 144, 152, 171, 216, 228, 288, 304, 342, 432, 456, 513, 608, 684, 864, 912, 1026, 1368, 1824, 2052, 2736, 4104, 5472, 8208, 16416. There are 48 integers that are factors of 16416. The greatest factor of 16416 is 16416.

4. How to Find the LCM of 16409 and 16416?

Answer:

Least Common Multiple of 16409 and 16416 = 269370144

Step 1: Find the prime factorization of 16409

16409 = 61 x 269

Step 2: Find the prime factorization of 16416

16416 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 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 = 269370144 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19 x 61 x 269

Step 4: Therefore, the least common multiple of 16409 and 16416 is 269370144.