Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7074 and 7080 the smallest integer that is 8347320 that is divisible by both numbers.
Least Common Multiple (LCM) of 7074 and 7080 is 8347320.
LCM(7074,7080) = 8347320
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 7074 and 7080. First we will calculate the prime factors of 7074 and 7080.
Prime Factorization of 7074
2 | 7074 |
3 | 3537 |
3 | 1179 |
3 | 393 |
131 | 131 |
1 |
Prime factors of 7074 are 2, 3,131. Prime factorization of 7074 in exponential form is:
7074 = 21×33×1311
Prime Factorization of 7080
2 | 7080 |
2 | 3540 |
2 | 1770 |
3 | 885 |
5 | 295 |
59 | 59 |
1 |
Prime factors of 7080 are 2, 3, 5,59. Prime factorization of 7080 in exponential form is:
7080 = 23×31×51×591
Now multiplying the highest exponent prime factors to calculate the LCM of 7074 and 7080.
LCM(7074,7080) = 23×33×51×591×1311
LCM(7074,7080) = 8347320
Factors of 7074
List of positive integer factors of 7074 that divides 7074 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54, 131, 262, 393, 786, 1179, 2358, 3537, 7074
Factors of 7080
List of positive integer factors of 7080 that divides 7080 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 59, 60, 118, 120, 177, 236, 295, 354, 472, 590, 708, 885, 1180, 1416, 1770, 2360, 3540, 7080
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7074 and 7080, than apply into the LCM equation.
GCF(7074,7080) = 6
LCM(7074,7080) = ( 7074 × 7080) / 6
LCM(7074,7080) = 50083920 / 6
LCM(7074,7080) = 8347320
(i) The LCM of 7080 and 7074 is associative
LCM of 7074 and 7080 = LCM of 7080 and 7074
1. What is the LCM of 7074 and 7080?
Answer: LCM of 7074 and 7080 is 8347320.
2. What are the Factors of 7074?
Answer: Factors of 7074 are 1, 2, 3, 6, 9, 18, 27, 54, 131, 262, 393, 786, 1179, 2358, 3537, 7074. There are 16 integers that are factors of 7074. The greatest factor of 7074 is 7074.
3. What are the Factors of 7080?
Answer: Factors of 7080 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 59, 60, 118, 120, 177, 236, 295, 354, 472, 590, 708, 885, 1180, 1416, 1770, 2360, 3540, 7080. There are 32 integers that are factors of 7080. The greatest factor of 7080 is 7080.
4. How to Find the LCM of 7074 and 7080?
Answer:
Least Common Multiple of 7074 and 7080 = 8347320
Step 1: Find the prime factorization of 7074
7074 = 2 x 3 x 3 x 3 x 131
Step 2: Find the prime factorization of 7080
7080 = 2 x 2 x 2 x 3 x 5 x 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8347320 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 59 x 131
Step 4: Therefore, the least common multiple of 7074 and 7080 is 8347320.