Least Common Multiple of 17208 and 17214

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 17214 the smallest integer that is 49369752 that is divisible by both numbers.

Least Common Multiple (LCM) of 17208 and 17214 is 49369752.

LCM(17208,17214) = 49369752

LCM of 17208 and 17214

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

LCM of:
and

Least Common Multiple of 17208 and 17214

LCM of 17208 and 17214 is 49369752

Least common multiple can be found by multiplying the highest exponent prime factors of 17208 and 17214. First we will calculate the prime factors of 17208 and 17214.

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 17214


2 17214
3 8607
19 2869
151 151
1

Prime factors of 17214 are 2, 3, 19,151. Prime factorization of 17214 in exponential form is:

17214 = 21×31×191×1511

Now multiplying the highest exponent prime factors to calculate the LCM of 17208 and 17214.

LCM(17208,17214) = 23×32×191×1511×2391
LCM(17208,17214) = 49369752

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 17214

List of positive integer factors of 17214 that divides 17214 without a remainder.

1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607, 17214

Least Common Multiple of 17208 and 17214 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 17214, than apply into the LCM equation.

GCF(17208,17214) = 6
LCM(17208,17214) = ( 17208 × 17214) / 6
LCM(17208,17214) = 296218512 / 6
LCM(17208,17214) = 49369752

Properties of LCM 17208 and 17214

(i) The LCM of 17214 and 17208 is associative

LCM of 17208 and 17214 = LCM of 17214 and 17208

Related Least Common Multiples of 17208

Related Least Common Multiples of 17214

Frequently Asked Questions on LCM of 17208 and 17214

1. What is the LCM of 17208 and 17214?

Answer: LCM of 17208 and 17214 is 49369752.

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 17214?

Answer: Factors of 17214 are 1, 2, 3, 6, 19, 38, 57, 114, 151, 302, 453, 906, 2869, 5738, 8607, 17214. There are 16 integers that are factors of 17214. The greatest factor of 17214 is 17214.

4. How to Find the LCM of 17208 and 17214?

Answer:

Least Common Multiple of 17208 and 17214 = 49369752

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 17214

17214 = 2 x 3 x 19 x 151

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

LCM = 49369752 = 2 x 2 x 2 x 3 x 3 x 19 x 151 x 239

Step 4: Therefore, the least common multiple of 17208 and 17214 is 49369752.