Least Common Multiple of 17212 and 17219

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

• Least Common Multiple of 17212 and 17219 by Prime method
• Least Common Multiple of 17212 and 17219 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17212 and 17219. First we will calculate the prime factors of 17212 and 17219.

Prime Factorization of 17212

Prime factors of 17212 are 2, 13,331. Prime factorization of 17212 in exponential form is:

17212 = 2²×13¹×331¹

Prime Factorization of 17219

Prime factors of 17219 are 67,257. Prime factorization of 17219 in exponential form is:

17219 = 67¹×257¹

Now multiplying the highest exponent prime factors to calculate the LCM of 17212 and 17219.

LCM(17212,17219) = 2²×13¹×67¹×257¹×331¹
LCM(17212,17219) = 296373428

Factors of 17212

List of positive integer factors of 17212 that divides 17212 without a remainder.

1, 2, 4, 13, 26, 52, 331, 662, 1324, 4303, 8606, 17212

Factors of 17219

List of positive integer factors of 17219 that divides 17219 without a remainder.

1, 67, 257, 17219

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17212 and 17219, than apply into the LCM equation.

GCF(17212,17219) = 1
LCM(17212,17219) = ( 17212 × 17219) / 1
LCM(17212,17219) = 296373428 / 1
LCM(17212,17219) = 296373428

(i) The LCM of 17219 and 17212 is associative

LCM of 17212 and 17219 = LCM of 17219 and 17212

1. What is the LCM of 17212 and 17219?

Answer: LCM of 17212 and 17219 is 296373428.

2. What are the Factors of 17212?

Answer: Factors of 17212 are 1, 2, 4, 13, 26, 52, 331, 662, 1324, 4303, 8606, 17212. There are 12 integers that are factors of 17212. The greatest factor of 17212 is 17212.

3. What are the Factors of 17219?

Answer: Factors of 17219 are 1, 67, 257, 17219. There are 4 integers that are factors of 17219. The greatest factor of 17219 is 17219.

4. How to Find the LCM of 17212 and 17219?

Answer:

Least Common Multiple of 17212 and 17219 = 296373428

Step 1: Find the prime factorization of 17212

17212 = 2 x 2 x 13 x 331

Step 2: Find the prime factorization of 17219

17219 = 67 x 257

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

LCM = 296373428 = 2 x 2 x 13 x 67 x 257 x 331

Step 4: Therefore, the least common multiple of 17212 and 17219 is 296373428.