Least Common Multiple of 17208 and 17216

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 17208 and 17216 the smallest integer that is 37031616 that is divisible by both numbers.

Least Common Multiple (LCM) of 17208 and 17216 is 37031616.

LCM(17208,17216) = 37031616

LCM of 17208 and 17216

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

LCM of:
and

Least Common Multiple of 17208 and 17216

LCM of 17208 and 17216 is 37031616

Least common multiple can be found by multiplying the highest exponent prime factors of 17208 and 17216. First we will calculate the prime factors of 17208 and 17216.

Prime Factorization of 17208


2 17208
2 8604
2 4302
3 2151
3 717
239 239
1

Prime factors of 17208 are 2, 3,239. Prime factorization of 17208 in exponential form is:

17208 = 23×32×2391

Prime Factorization of 17216


2 17216
2 8608
2 4304
2 2152
2 1076
2 538
269 269
1

Prime factors of 17216 are 2,269. Prime factorization of 17216 in exponential form is:

17216 = 26×2691

Now multiplying the highest exponent prime factors to calculate the LCM of 17208 and 17216.

LCM(17208,17216) = 26×32×2391×2691
LCM(17208,17216) = 37031616

Factors of 17208

List of positive integer factors of 17208 that divides 17208 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 4302, 5736, 8604, 17208

Factors of 17216

List of positive integer factors of 17216 that divides 17216 without a remainder.

1, 2, 4, 8, 16, 32, 64, 269, 538, 1076, 2152, 4304, 8608, 17216

Least Common Multiple of 17208 and 17216 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17208 and 17216, than apply into the LCM equation.

GCF(17208,17216) = 8
LCM(17208,17216) = ( 17208 × 17216) / 8
LCM(17208,17216) = 296252928 / 8
LCM(17208,17216) = 37031616

Properties of LCM 17208 and 17216

(i) The LCM of 17216 and 17208 is associative

LCM of 17208 and 17216 = LCM of 17216 and 17208

Related Least Common Multiples of 17208

Related Least Common Multiples of 17216

Frequently Asked Questions on LCM of 17208 and 17216

1. What is the LCM of 17208 and 17216?

Answer: LCM of 17208 and 17216 is 37031616.

2. What are the Factors of 17208?

Answer: Factors of 17208 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 239, 478, 717, 956, 1434, 1912, 2151, 2868, 4302, 5736, 8604, 17208. There are 24 integers that are factors of 17208. The greatest factor of 17208 is 17208.

3. What are the Factors of 17216?

Answer: Factors of 17216 are 1, 2, 4, 8, 16, 32, 64, 269, 538, 1076, 2152, 4304, 8608, 17216. There are 14 integers that are factors of 17216. The greatest factor of 17216 is 17216.

4. How to Find the LCM of 17208 and 17216?

Answer:

Least Common Multiple of 17208 and 17216 = 37031616

Step 1: Find the prime factorization of 17208

17208 = 2 x 2 x 2 x 3 x 3 x 239

Step 2: Find the prime factorization of 17216

17216 = 2 x 2 x 2 x 2 x 2 x 2 x 269

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

LCM = 37031616 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 239 x 269

Step 4: Therefore, the least common multiple of 17208 and 17216 is 37031616.