Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 8342 and 8350 the smallest integer that is 34827850 that is divisible by both numbers.
Least Common Multiple (LCM) of 8342 and 8350 is 34827850.
LCM(8342,8350) = 34827850
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 8342 and 8350. First we will calculate the prime factors of 8342 and 8350.
Prime Factorization of 8342
2 | 8342 |
43 | 4171 |
97 | 97 |
1 |
Prime factors of 8342 are 2, 43,97. Prime factorization of 8342 in exponential form is:
8342 = 21×431×971
Prime Factorization of 8350
2 | 8350 |
5 | 4175 |
5 | 835 |
167 | 167 |
1 |
Prime factors of 8350 are 2, 5,167. Prime factorization of 8350 in exponential form is:
8350 = 21×52×1671
Now multiplying the highest exponent prime factors to calculate the LCM of 8342 and 8350.
LCM(8342,8350) = 21×52×431×971×1671
LCM(8342,8350) = 34827850
Factors of 8342
List of positive integer factors of 8342 that divides 8342 without a remainder.
1, 2, 43, 86, 97, 194, 4171, 8342
Factors of 8350
List of positive integer factors of 8350 that divides 8350 without a remainder.
1, 2, 5, 10, 25, 50, 167, 334, 835, 1670, 4175, 8350
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8342 and 8350, than apply into the LCM equation.
GCF(8342,8350) = 2
LCM(8342,8350) = ( 8342 × 8350) / 2
LCM(8342,8350) = 69655700 / 2
LCM(8342,8350) = 34827850
(i) The LCM of 8350 and 8342 is associative
LCM of 8342 and 8350 = LCM of 8350 and 8342
1. What is the LCM of 8342 and 8350?
Answer: LCM of 8342 and 8350 is 34827850.
2. What are the Factors of 8342?
Answer: Factors of 8342 are 1, 2, 43, 86, 97, 194, 4171, 8342. There are 8 integers that are factors of 8342. The greatest factor of 8342 is 8342.
3. What are the Factors of 8350?
Answer: Factors of 8350 are 1, 2, 5, 10, 25, 50, 167, 334, 835, 1670, 4175, 8350. There are 12 integers that are factors of 8350. The greatest factor of 8350 is 8350.
4. How to Find the LCM of 8342 and 8350?
Answer:
Least Common Multiple of 8342 and 8350 = 34827850
Step 1: Find the prime factorization of 8342
8342 = 2 x 43 x 97
Step 2: Find the prime factorization of 8350
8350 = 2 x 5 x 5 x 167
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 34827850 = 2 x 5 x 5 x 43 x 97 x 167
Step 4: Therefore, the least common multiple of 8342 and 8350 is 34827850.