Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 10178 and 10183 the smallest integer that is 103642574 that is divisible by both numbers.
Least Common Multiple (LCM) of 10178 and 10183 is 103642574.
LCM(10178,10183) = 103642574
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 10178 and 10183. First we will calculate the prime factors of 10178 and 10183.
Prime Factorization of 10178
2 | 10178 |
7 | 5089 |
727 | 727 |
1 |
Prime factors of 10178 are 2, 7,727. Prime factorization of 10178 in exponential form is:
10178 = 21×71×7271
Prime Factorization of 10183
17 | 10183 |
599 | 599 |
1 |
Prime factors of 10183 are 17,599. Prime factorization of 10183 in exponential form is:
10183 = 171×5991
Now multiplying the highest exponent prime factors to calculate the LCM of 10178 and 10183.
LCM(10178,10183) = 21×71×171×5991×7271
LCM(10178,10183) = 103642574
Factors of 10178
List of positive integer factors of 10178 that divides 10178 without a remainder.
1, 2, 7, 14, 727, 1454, 5089, 10178
Factors of 10183
List of positive integer factors of 10183 that divides 10183 without a remainder.
1, 17, 599, 10183
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10178 and 10183, than apply into the LCM equation.
GCF(10178,10183) = 1
LCM(10178,10183) = ( 10178 × 10183) / 1
LCM(10178,10183) = 103642574 / 1
LCM(10178,10183) = 103642574
(i) The LCM of 10183 and 10178 is associative
LCM of 10178 and 10183 = LCM of 10183 and 10178
1. What is the LCM of 10178 and 10183?
Answer: LCM of 10178 and 10183 is 103642574.
2. What are the Factors of 10178?
Answer: Factors of 10178 are 1, 2, 7, 14, 727, 1454, 5089, 10178. There are 8 integers that are factors of 10178. The greatest factor of 10178 is 10178.
3. What are the Factors of 10183?
Answer: Factors of 10183 are 1, 17, 599, 10183. There are 4 integers that are factors of 10183. The greatest factor of 10183 is 10183.
4. How to Find the LCM of 10178 and 10183?
Answer:
Least Common Multiple of 10178 and 10183 = 103642574
Step 1: Find the prime factorization of 10178
10178 = 2 x 7 x 727
Step 2: Find the prime factorization of 10183
10183 = 17 x 599
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 103642574 = 2 x 7 x 17 x 599 x 727
Step 4: Therefore, the least common multiple of 10178 and 10183 is 103642574.