Least Common Multiple of 5208 and 5214

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 5208 and 5214 the smallest integer that is 4525752 that is divisible by both numbers.

Least Common Multiple (LCM) of 5208 and 5214 is 4525752.

LCM(5208,5214) = 4525752

LCM of 5208 and 5214

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

LCM of:
and

Least Common Multiple of 5208 and 5214

LCM of 5208 and 5214 is 4525752

Least common multiple can be found by multiplying the highest exponent prime factors of 5208 and 5214. First we will calculate the prime factors of 5208 and 5214.

Prime Factorization of 5208


2 5208
2 2604
2 1302
3 651
7 217
31 31
1

Prime factors of 5208 are 2, 3, 7,31. Prime factorization of 5208 in exponential form is:

5208 = 23×31×71×311

Prime Factorization of 5214


2 5214
3 2607
11 869
79 79
1

Prime factors of 5214 are 2, 3, 11,79. Prime factorization of 5214 in exponential form is:

5214 = 21×31×111×791

Now multiplying the highest exponent prime factors to calculate the LCM of 5208 and 5214.

LCM(5208,5214) = 23×31×71×111×311×791
LCM(5208,5214) = 4525752

Factors of 5208

List of positive integer factors of 5208 that divides 5208 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 31, 42, 56, 62, 84, 93, 124, 168, 186, 217, 248, 372, 434, 651, 744, 868, 1302, 1736, 2604, 5208

Factors of 5214

List of positive integer factors of 5214 that divides 5214 without a remainder.

1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607, 5214

Least Common Multiple of 5208 and 5214 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5208 and 5214, than apply into the LCM equation.

GCF(5208,5214) = 6
LCM(5208,5214) = ( 5208 × 5214) / 6
LCM(5208,5214) = 27154512 / 6
LCM(5208,5214) = 4525752

Properties of LCM 5208 and 5214

(i) The LCM of 5214 and 5208 is associative

LCM of 5208 and 5214 = LCM of 5214 and 5208

Related Least Common Multiples of 5208

Related Least Common Multiples of 5214

Frequently Asked Questions on LCM of 5208 and 5214

1. What is the LCM of 5208 and 5214?

Answer: LCM of 5208 and 5214 is 4525752.

2. What are the Factors of 5208?

Answer: Factors of 5208 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 31, 42, 56, 62, 84, 93, 124, 168, 186, 217, 248, 372, 434, 651, 744, 868, 1302, 1736, 2604, 5208. There are 32 integers that are factors of 5208. The greatest factor of 5208 is 5208.

3. What are the Factors of 5214?

Answer: Factors of 5214 are 1, 2, 3, 6, 11, 22, 33, 66, 79, 158, 237, 474, 869, 1738, 2607, 5214. There are 16 integers that are factors of 5214. The greatest factor of 5214 is 5214.

4. How to Find the LCM of 5208 and 5214?

Answer:

Least Common Multiple of 5208 and 5214 = 4525752

Step 1: Find the prime factorization of 5208

5208 = 2 x 2 x 2 x 3 x 7 x 31

Step 2: Find the prime factorization of 5214

5214 = 2 x 3 x 11 x 79

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

LCM = 4525752 = 2 x 2 x 2 x 3 x 7 x 11 x 31 x 79

Step 4: Therefore, the least common multiple of 5208 and 5214 is 4525752.