Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 39000 and 39008 the smallest integer that is 190164000 that is divisible by both numbers.
Least Common Multiple (LCM) of 39000 and 39008 is 190164000.
LCM(39000,39008) = 190164000
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 39000 and 39008. First we will calculate the prime factors of 39000 and 39008.
Prime Factorization of 39000
2 | 39000 |
2 | 19500 |
2 | 9750 |
3 | 4875 |
5 | 1625 |
5 | 325 |
5 | 65 |
13 | 13 |
1 |
Prime factors of 39000 are 2, 3, 5,13. Prime factorization of 39000 in exponential form is:
39000 = 23×31×53×131
Prime Factorization of 39008
2 | 39008 |
2 | 19504 |
2 | 9752 |
2 | 4876 |
2 | 2438 |
23 | 1219 |
53 | 53 |
1 |
Prime factors of 39008 are 2, 23,53. Prime factorization of 39008 in exponential form is:
39008 = 25×231×531
Now multiplying the highest exponent prime factors to calculate the LCM of 39000 and 39008.
LCM(39000,39008) = 25×31×53×131×231×531
LCM(39000,39008) = 190164000
Factors of 39000
List of positive integer factors of 39000 that divides 39000 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 25, 26, 30, 39, 40, 50, 52, 60, 65, 75, 78, 100, 104, 120, 125, 130, 150, 156, 195, 200, 250, 260, 300, 312, 325, 375, 390, 500, 520, 600, 650, 750, 780, 975, 1000, 1300, 1500, 1560, 1625, 1950, 2600, 3000, 3250, 3900, 4875, 6500, 7800, 9750, 13000, 19500, 39000
Factors of 39008
List of positive integer factors of 39008 that divides 39008 without a remainder.
1, 2, 4, 8, 16, 23, 32, 46, 53, 92, 106, 184, 212, 368, 424, 736, 848, 1219, 1696, 2438, 4876, 9752, 19504, 39008
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 39000 and 39008, than apply into the LCM equation.
GCF(39000,39008) = 8
LCM(39000,39008) = ( 39000 × 39008) / 8
LCM(39000,39008) = 1521312000 / 8
LCM(39000,39008) = 190164000
(i) The LCM of 39008 and 39000 is associative
LCM of 39000 and 39008 = LCM of 39008 and 39000
1. What is the LCM of 39000 and 39008?
Answer: LCM of 39000 and 39008 is 190164000.
2. What are the Factors of 39000?
Answer: Factors of 39000 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 13, 15, 20, 24, 25, 26, 30, 39, 40, 50, 52, 60, 65, 75, 78, 100, 104, 120, 125, 130, 150, 156, 195, 200, 250, 260, 300, 312, 325, 375, 390, 500, 520, 600, 650, 750, 780, 975, 1000, 1300, 1500, 1560, 1625, 1950, 2600, 3000, 3250, 3900, 4875, 6500, 7800, 9750, 13000, 19500, 39000. There are 64 integers that are factors of 39000. The greatest factor of 39000 is 39000.
3. What are the Factors of 39008?
Answer: Factors of 39008 are 1, 2, 4, 8, 16, 23, 32, 46, 53, 92, 106, 184, 212, 368, 424, 736, 848, 1219, 1696, 2438, 4876, 9752, 19504, 39008. There are 24 integers that are factors of 39008. The greatest factor of 39008 is 39008.
4. How to Find the LCM of 39000 and 39008?
Answer:
Least Common Multiple of 39000 and 39008 = 190164000
Step 1: Find the prime factorization of 39000
39000 = 2 x 2 x 2 x 3 x 5 x 5 x 5 x 13
Step 2: Find the prime factorization of 39008
39008 = 2 x 2 x 2 x 2 x 2 x 23 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 190164000 = 2 x 2 x 2 x 2 x 2 x 3 x 5 x 5 x 5 x 13 x 23 x 53
Step 4: Therefore, the least common multiple of 39000 and 39008 is 190164000.