Least Common Multiple of 17206 and 17214

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

• Least Common Multiple of 17206 and 17214 by Prime method
• Least Common Multiple of 17206 and 17214 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17206 and 17214. First we will calculate the prime factors of 17206 and 17214.

Prime Factorization of 17206

Prime factors of 17206 are 2, 7,1229. Prime factorization of 17206 in exponential form is:

17206 = 2¹×7¹×1229¹

Prime Factorization of 17214

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 17206 and 17214.

LCM(17206,17214) = 2¹×3¹×7¹×19¹×151¹×1229¹
LCM(17206,17214) = 148092042

Factors of 17206

List of positive integer factors of 17206 that divides 17206 without a remainder.

1, 2, 7, 14, 1229, 2458, 8603, 17206

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

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17206 and 17214, than apply into the LCM equation.

GCF(17206,17214) = 2
LCM(17206,17214) = ( 17206 × 17214) / 2
LCM(17206,17214) = 296184084 / 2
LCM(17206,17214) = 148092042

(i) The LCM of 17214 and 17206 is associative

LCM of 17206 and 17214 = LCM of 17214 and 17206

1. What is the LCM of 17206 and 17214?

Answer: LCM of 17206 and 17214 is 148092042.

2. What are the Factors of 17206?

Answer: Factors of 17206 are 1, 2, 7, 14, 1229, 2458, 8603, 17206. There are 8 integers that are factors of 17206. The greatest factor of 17206 is 17206.

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 17206 and 17214?

Answer:

Least Common Multiple of 17206 and 17214 = 148092042

Step 1: Find the prime factorization of 17206

17206 = 2 x 7 x 1229

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 = 148092042 = 2 x 3 x 7 x 19 x 151 x 1229

Step 4: Therefore, the least common multiple of 17206 and 17214 is 148092042.