Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 38 and 41 the smallest integer that is 1558 that is divisible by both numbers.
Least Common Multiple (LCM) of 38 and 41 is 1558.
LCM(38,41) = 1558
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 38 and 41. First we will calculate the prime factors of 38 and 41.
Prime Factorization of 38
2 | 38 |
19 | 19 |
1 |
Prime factors of 38 are 2,19. Prime factorization of 38 in exponential form is:
38 = 21×191
Prime Factorization of 41
41 | 41 |
1 |
Prime factors of 41 are 41. Prime factorization of 41 in exponential form is:
41 = 411
Now multiplying the highest exponent prime factors to calculate the LCM of 38 and 41.
LCM(38,41) = 21×191×411
LCM(38,41) = 1558
Factors of 38
List of positive integer factors of 38 that divides 38 without a remainder.
1, 2, 19, 38
Factors of 41
List of positive integer factors of 41 that divides 41 without a remainder.
1, 41
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 41, than apply into the LCM equation.
GCF(38,41) = 1
LCM(38,41) = ( 38 × 41) / 1
LCM(38,41) = 1558 / 1
LCM(38,41) = 1558
(i) The LCM of 41 and 38 is associative
LCM of 38 and 41 = LCM of 41 and 38
1. What is the LCM of 38 and 41?
Answer: LCM of 38 and 41 is 1558.
2. What are the Factors of 38?
Answer: Factors of 38 are 1, 2, 19, 38. There are 4 integers that are factors of 38. The greatest factor of 38 is 38.
3. What are the Factors of 41?
Answer: Factors of 41 are 1, 41. There are 2 integers that are factors of 41. The greatest factor of 41 is 41.
4. How to Find the LCM of 38 and 41?
Answer:
Least Common Multiple of 38 and 41 = 1558
Step 1: Find the prime factorization of 38
38 = 2 x 19
Step 2: Find the prime factorization of 41
41 = 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1558 = 2 x 19 x 41
Step 4: Therefore, the least common multiple of 38 and 41 is 1558.