Least Common Multiple of 17214 and 17221

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

• Least Common Multiple of 17214 and 17221 by Prime method
• Least Common Multiple of 17214 and 17221 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 17214 and 17221. First we will calculate the prime factors of 17214 and 17221.

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

Prime Factorization of 17221

Prime factors of 17221 are 17,1013. Prime factorization of 17221 in exponential form is:

17221 = 17¹×1013¹

Now multiplying the highest exponent prime factors to calculate the LCM of 17214 and 17221.

LCM(17214,17221) = 2¹×3¹×17¹×19¹×151¹×1013¹
LCM(17214,17221) = 296442294

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

Factors of 17221

List of positive integer factors of 17221 that divides 17221 without a remainder.

1, 17, 1013, 17221

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17214 and 17221, than apply into the LCM equation.

GCF(17214,17221) = 1
LCM(17214,17221) = ( 17214 × 17221) / 1
LCM(17214,17221) = 296442294 / 1
LCM(17214,17221) = 296442294

(i) The LCM of 17221 and 17214 is associative

LCM of 17214 and 17221 = LCM of 17221 and 17214

1. What is the LCM of 17214 and 17221?

Answer: LCM of 17214 and 17221 is 296442294.

2. 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.

3. What are the Factors of 17221?

Answer: Factors of 17221 are 1, 17, 1013, 17221. There are 4 integers that are factors of 17221. The greatest factor of 17221 is 17221.

4. How to Find the LCM of 17214 and 17221?

Answer:

Least Common Multiple of 17214 and 17221 = 296442294

Step 1: Find the prime factorization of 17214

17214 = 2 x 3 x 19 x 151

Step 2: Find the prime factorization of 17221

17221 = 17 x 1013

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

LCM = 296442294 = 2 x 3 x 17 x 19 x 151 x 1013

Step 4: Therefore, the least common multiple of 17214 and 17221 is 296442294.