Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 39208 and 39215 the smallest integer that is 1537541720 that is divisible by both numbers.
Least Common Multiple (LCM) of 39208 and 39215 is 1537541720.
LCM(39208,39215) = 1537541720
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 39208 and 39215. First we will calculate the prime factors of 39208 and 39215.
Prime Factorization of 39208
2 | 39208 |
2 | 19604 |
2 | 9802 |
13 | 4901 |
13 | 377 |
29 | 29 |
1 |
Prime factors of 39208 are 2, 13,29. Prime factorization of 39208 in exponential form is:
39208 = 23×132×291
Prime Factorization of 39215
5 | 39215 |
11 | 7843 |
23 | 713 |
31 | 31 |
1 |
Prime factors of 39215 are 5, 11, 23,31. Prime factorization of 39215 in exponential form is:
39215 = 51×111×231×311
Now multiplying the highest exponent prime factors to calculate the LCM of 39208 and 39215.
LCM(39208,39215) = 23×51×111×132×231×291×311
LCM(39208,39215) = 1537541720
Factors of 39208
List of positive integer factors of 39208 that divides 39208 without a remainder.
1, 2, 4, 8, 13, 26, 29, 52, 58, 104, 116, 169, 232, 338, 377, 676, 754, 1352, 1508, 3016, 4901, 9802, 19604, 39208
Factors of 39215
List of positive integer factors of 39215 that divides 39215 without a remainder.
1, 5, 11, 23, 31, 55, 115, 155, 253, 341, 713, 1265, 1705, 3565, 7843, 39215
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39208 and 39215, than apply into the LCM equation.
GCF(39208,39215) = 1
LCM(39208,39215) = ( 39208 × 39215) / 1
LCM(39208,39215) = 1537541720 / 1
LCM(39208,39215) = 1537541720
(i) The LCM of 39215 and 39208 is associative
LCM of 39208 and 39215 = LCM of 39215 and 39208
1. What is the LCM of 39208 and 39215?
Answer: LCM of 39208 and 39215 is 1537541720.
2. What are the Factors of 39208?
Answer: Factors of 39208 are 1, 2, 4, 8, 13, 26, 29, 52, 58, 104, 116, 169, 232, 338, 377, 676, 754, 1352, 1508, 3016, 4901, 9802, 19604, 39208. There are 24 integers that are factors of 39208. The greatest factor of 39208 is 39208.
3. What are the Factors of 39215?
Answer: Factors of 39215 are 1, 5, 11, 23, 31, 55, 115, 155, 253, 341, 713, 1265, 1705, 3565, 7843, 39215. There are 16 integers that are factors of 39215. The greatest factor of 39215 is 39215.
4. How to Find the LCM of 39208 and 39215?
Answer:
Least Common Multiple of 39208 and 39215 = 1537541720
Step 1: Find the prime factorization of 39208
39208 = 2 x 2 x 2 x 13 x 13 x 29
Step 2: Find the prime factorization of 39215
39215 = 5 x 11 x 23 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1537541720 = 2 x 2 x 2 x 5 x 11 x 13 x 13 x 23 x 29 x 31
Step 4: Therefore, the least common multiple of 39208 and 39215 is 1537541720.