Least Common Multiple of 17209 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 17209 and 17216 the smallest integer that is 296270144 that is divisible by both numbers.

Least Common Multiple (LCM) of 17209 and 17216 is 296270144.

LCM(17209,17216) = 296270144

LCM of 17209 and 17216

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

LCM of:
and

Least Common Multiple of 17209 and 17216

LCM of 17209 and 17216 is 296270144

Least common multiple can be found by multiplying the highest exponent prime factors of 17209 and 17216. First we will calculate the prime factors of 17209 and 17216.

Prime Factorization of 17209


17209 17209
1

Prime factors of 17209 are 17209. Prime factorization of 17209 in exponential form is:

17209 = 172091

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 17209 and 17216.

LCM(17209,17216) = 26×2691×172091
LCM(17209,17216) = 296270144

Factors of 17209

List of positive integer factors of 17209 that divides 17209 without a remainder.

1, 17209

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 17209 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 17209 and 17216, than apply into the LCM equation.

GCF(17209,17216) = 1
LCM(17209,17216) = ( 17209 × 17216) / 1
LCM(17209,17216) = 296270144 / 1
LCM(17209,17216) = 296270144

Properties of LCM 17209 and 17216

(i) The LCM of 17216 and 17209 is associative

LCM of 17209 and 17216 = LCM of 17216 and 17209

Related Least Common Multiples of 17209

Related Least Common Multiples of 17216

Frequently Asked Questions on LCM of 17209 and 17216

1. What is the LCM of 17209 and 17216?

Answer: LCM of 17209 and 17216 is 296270144.

2. What are the Factors of 17209?

Answer: Factors of 17209 are 1, 17209. There are 2 integers that are factors of 17209. The greatest factor of 17209 is 17209.

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 17209 and 17216?

Answer:

Least Common Multiple of 17209 and 17216 = 296270144

Step 1: Find the prime factorization of 17209

17209 = 17209

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 = 296270144 = 2 x 2 x 2 x 2 x 2 x 2 x 269 x 17209

Step 4: Therefore, the least common multiple of 17209 and 17216 is 296270144.