Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1940 and 1944 the smallest integer that is 942840 that is divisible by both numbers.
Least Common Multiple (LCM) of 1940 and 1944 is 942840.
LCM(1940,1944) = 942840
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 1940 and 1944. First we will calculate the prime factors of 1940 and 1944.
Prime Factorization of 1940
2 | 1940 |
2 | 970 |
5 | 485 |
97 | 97 |
1 |
Prime factors of 1940 are 2, 5,97. Prime factorization of 1940 in exponential form is:
1940 = 22×51×971
Prime Factorization of 1944
2 | 1944 |
2 | 972 |
2 | 486 |
3 | 243 |
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 1944 are 2,3. Prime factorization of 1944 in exponential form is:
1944 = 23×35
Now multiplying the highest exponent prime factors to calculate the LCM of 1940 and 1944.
LCM(1940,1944) = 23×35×51×971
LCM(1940,1944) = 942840
Factors of 1940
List of positive integer factors of 1940 that divides 1940 without a remainder.
1, 2, 4, 5, 10, 20, 97, 194, 388, 485, 970, 1940
Factors of 1944
List of positive integer factors of 1944 that divides 1944 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1940 and 1944, than apply into the LCM equation.
GCF(1940,1944) = 4
LCM(1940,1944) = ( 1940 × 1944) / 4
LCM(1940,1944) = 3771360 / 4
LCM(1940,1944) = 942840
(i) The LCM of 1944 and 1940 is associative
LCM of 1940 and 1944 = LCM of 1944 and 1940
1. What is the LCM of 1940 and 1944?
Answer: LCM of 1940 and 1944 is 942840.
2. What are the Factors of 1940?
Answer: Factors of 1940 are 1, 2, 4, 5, 10, 20, 97, 194, 388, 485, 970, 1940. There are 12 integers that are factors of 1940. The greatest factor of 1940 is 1940.
3. What are the Factors of 1944?
Answer: Factors of 1944 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 243, 324, 486, 648, 972, 1944. There are 24 integers that are factors of 1944. The greatest factor of 1944 is 1944.
4. How to Find the LCM of 1940 and 1944?
Answer:
Least Common Multiple of 1940 and 1944 = 942840
Step 1: Find the prime factorization of 1940
1940 = 2 x 2 x 5 x 97
Step 2: Find the prime factorization of 1944
1944 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 942840 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 5 x 97
Step 4: Therefore, the least common multiple of 1940 and 1944 is 942840.