Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 221837 and 221840 the smallest integer that is 49212320080 that is divisible by both numbers.
Least Common Multiple (LCM) of 221837 and 221840 is 49212320080.
LCM(221837,221840) = 49212320080
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 221837 and 221840. First we will calculate the prime factors of 221837 and 221840.
Prime Factorization of 221837
7 | 221837 |
11 | 31691 |
43 | 2881 |
67 | 67 |
1 |
Prime factors of 221837 are 7, 11, 43,67. Prime factorization of 221837 in exponential form is:
221837 = 71×111×431×671
Prime Factorization of 221840
2 | 221840 |
2 | 110920 |
2 | 55460 |
2 | 27730 |
5 | 13865 |
47 | 2773 |
59 | 59 |
1 |
Prime factors of 221840 are 2, 5, 47,59. Prime factorization of 221840 in exponential form is:
221840 = 24×51×471×591
Now multiplying the highest exponent prime factors to calculate the LCM of 221837 and 221840.
LCM(221837,221840) = 24×51×71×111×431×471×591×671
LCM(221837,221840) = 49212320080
Factors of 221837
List of positive integer factors of 221837 that divides 221837 without a remainder.
1, 7, 11, 43, 67, 77, 301, 469, 473, 737, 2881, 3311, 5159, 20167, 31691, 221837
Factors of 221840
List of positive integer factors of 221840 that divides 221840 without a remainder.
1, 2, 4, 5, 8, 10, 16, 20, 40, 47, 59, 80, 94, 118, 188, 235, 236, 295, 376, 470, 472, 590, 752, 940, 944, 1180, 1880, 2360, 2773, 3760, 4720, 5546, 11092, 13865, 22184, 27730, 44368, 55460, 110920, 221840
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 221837 and 221840, than apply into the LCM equation.
GCF(221837,221840) = 1
LCM(221837,221840) = ( 221837 × 221840) / 1
LCM(221837,221840) = 49212320080 / 1
LCM(221837,221840) = 49212320080
(i) The LCM of 221840 and 221837 is associative
LCM of 221837 and 221840 = LCM of 221840 and 221837
1. What is the LCM of 221837 and 221840?
Answer: LCM of 221837 and 221840 is 49212320080.
2. What are the Factors of 221837?
Answer: Factors of 221837 are 1, 7, 11, 43, 67, 77, 301, 469, 473, 737, 2881, 3311, 5159, 20167, 31691, 221837. There are 16 integers that are factors of 221837. The greatest factor of 221837 is 221837.
3. What are the Factors of 221840?
Answer: Factors of 221840 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 47, 59, 80, 94, 118, 188, 235, 236, 295, 376, 470, 472, 590, 752, 940, 944, 1180, 1880, 2360, 2773, 3760, 4720, 5546, 11092, 13865, 22184, 27730, 44368, 55460, 110920, 221840. There are 40 integers that are factors of 221840. The greatest factor of 221840 is 221840.
4. How to Find the LCM of 221837 and 221840?
Answer:
Least Common Multiple of 221837 and 221840 = 49212320080
Step 1: Find the prime factorization of 221837
221837 = 7 x 11 x 43 x 67
Step 2: Find the prime factorization of 221840
221840 = 2 x 2 x 2 x 2 x 5 x 47 x 59
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 49212320080 = 2 x 2 x 2 x 2 x 5 x 7 x 11 x 43 x 47 x 59 x 67
Step 4: Therefore, the least common multiple of 221837 and 221840 is 49212320080.