Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8471 and 8478 the smallest integer that is 71817138 that is divisible by both numbers.
Least Common Multiple (LCM) of 8471 and 8478 is 71817138.
LCM(8471,8478) = 71817138
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 8471 and 8478. First we will calculate the prime factors of 8471 and 8478.
Prime Factorization of 8471
43 | 8471 |
197 | 197 |
1 |
Prime factors of 8471 are 43,197. Prime factorization of 8471 in exponential form is:
8471 = 431×1971
Prime Factorization of 8478
2 | 8478 |
3 | 4239 |
3 | 1413 |
3 | 471 |
157 | 157 |
1 |
Prime factors of 8478 are 2, 3,157. Prime factorization of 8478 in exponential form is:
8478 = 21×33×1571
Now multiplying the highest exponent prime factors to calculate the LCM of 8471 and 8478.
LCM(8471,8478) = 21×33×431×1571×1971
LCM(8471,8478) = 71817138
Factors of 8471
List of positive integer factors of 8471 that divides 8471 without a remainder.
1, 43, 197, 8471
Factors of 8478
List of positive integer factors of 8478 that divides 8478 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54, 157, 314, 471, 942, 1413, 2826, 4239, 8478
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8471 and 8478, than apply into the LCM equation.
GCF(8471,8478) = 1
LCM(8471,8478) = ( 8471 × 8478) / 1
LCM(8471,8478) = 71817138 / 1
LCM(8471,8478) = 71817138
(i) The LCM of 8478 and 8471 is associative
LCM of 8471 and 8478 = LCM of 8478 and 8471
1. What is the LCM of 8471 and 8478?
Answer: LCM of 8471 and 8478 is 71817138.
2. What are the Factors of 8471?
Answer: Factors of 8471 are 1, 43, 197, 8471. There are 4 integers that are factors of 8471. The greatest factor of 8471 is 8471.
3. What are the Factors of 8478?
Answer: Factors of 8478 are 1, 2, 3, 6, 9, 18, 27, 54, 157, 314, 471, 942, 1413, 2826, 4239, 8478. There are 16 integers that are factors of 8478. The greatest factor of 8478 is 8478.
4. How to Find the LCM of 8471 and 8478?
Answer:
Least Common Multiple of 8471 and 8478 = 71817138
Step 1: Find the prime factorization of 8471
8471 = 43 x 197
Step 2: Find the prime factorization of 8478
8478 = 2 x 3 x 3 x 3 x 157
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 71817138 = 2 x 3 x 3 x 3 x 43 x 157 x 197
Step 4: Therefore, the least common multiple of 8471 and 8478 is 71817138.