Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7176 and 7182 the smallest integer that is 8589672 that is divisible by both numbers.
Least Common Multiple (LCM) of 7176 and 7182 is 8589672.
LCM(7176,7182) = 8589672
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 7176 and 7182. First we will calculate the prime factors of 7176 and 7182.
Prime Factorization of 7176
2 | 7176 |
2 | 3588 |
2 | 1794 |
3 | 897 |
13 | 299 |
23 | 23 |
1 |
Prime factors of 7176 are 2, 3, 13,23. Prime factorization of 7176 in exponential form is:
7176 = 23×31×131×231
Prime Factorization of 7182
2 | 7182 |
3 | 3591 |
3 | 1197 |
3 | 399 |
7 | 133 |
19 | 19 |
1 |
Prime factors of 7182 are 2, 3, 7,19. Prime factorization of 7182 in exponential form is:
7182 = 21×33×71×191
Now multiplying the highest exponent prime factors to calculate the LCM of 7176 and 7182.
LCM(7176,7182) = 23×33×71×131×191×231
LCM(7176,7182) = 8589672
Factors of 7176
List of positive integer factors of 7176 that divides 7176 without a remainder.
1, 2, 3, 4, 6, 8, 12, 13, 23, 24, 26, 39, 46, 52, 69, 78, 92, 104, 138, 156, 184, 276, 299, 312, 552, 598, 897, 1196, 1794, 2392, 3588, 7176
Factors of 7182
List of positive integer factors of 7182 that divides 7182 without a remainder.
1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 114, 126, 133, 171, 189, 266, 342, 378, 399, 513, 798, 1026, 1197, 2394, 3591, 7182
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7176 and 7182, than apply into the LCM equation.
GCF(7176,7182) = 6
LCM(7176,7182) = ( 7176 × 7182) / 6
LCM(7176,7182) = 51538032 / 6
LCM(7176,7182) = 8589672
(i) The LCM of 7182 and 7176 is associative
LCM of 7176 and 7182 = LCM of 7182 and 7176
1. What is the LCM of 7176 and 7182?
Answer: LCM of 7176 and 7182 is 8589672.
2. What are the Factors of 7176?
Answer: Factors of 7176 are 1, 2, 3, 4, 6, 8, 12, 13, 23, 24, 26, 39, 46, 52, 69, 78, 92, 104, 138, 156, 184, 276, 299, 312, 552, 598, 897, 1196, 1794, 2392, 3588, 7176. There are 32 integers that are factors of 7176. The greatest factor of 7176 is 7176.
3. What are the Factors of 7182?
Answer: Factors of 7182 are 1, 2, 3, 6, 7, 9, 14, 18, 19, 21, 27, 38, 42, 54, 57, 63, 114, 126, 133, 171, 189, 266, 342, 378, 399, 513, 798, 1026, 1197, 2394, 3591, 7182. There are 32 integers that are factors of 7182. The greatest factor of 7182 is 7182.
4. How to Find the LCM of 7176 and 7182?
Answer:
Least Common Multiple of 7176 and 7182 = 8589672
Step 1: Find the prime factorization of 7176
7176 = 2 x 2 x 2 x 3 x 13 x 23
Step 2: Find the prime factorization of 7182
7182 = 2 x 3 x 3 x 3 x 7 x 19
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8589672 = 2 x 2 x 2 x 3 x 3 x 3 x 7 x 13 x 19 x 23
Step 4: Therefore, the least common multiple of 7176 and 7182 is 8589672.