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 1942 the smallest integer that is 1883740 that is divisible by both numbers.
Least Common Multiple (LCM) of 1940 and 1942 is 1883740.
LCM(1940,1942) = 1883740
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 1942. First we will calculate the prime factors of 1940 and 1942.
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 1942
2 | 1942 |
971 | 971 |
1 |
Prime factors of 1942 are 2,971. Prime factorization of 1942 in exponential form is:
1942 = 21×9711
Now multiplying the highest exponent prime factors to calculate the LCM of 1940 and 1942.
LCM(1940,1942) = 22×51×971×9711
LCM(1940,1942) = 1883740
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 1942
List of positive integer factors of 1942 that divides 1942 without a remainder.
1, 2, 971, 1942
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1940 and 1942, than apply into the LCM equation.
GCF(1940,1942) = 2
LCM(1940,1942) = ( 1940 × 1942) / 2
LCM(1940,1942) = 3767480 / 2
LCM(1940,1942) = 1883740
(i) The LCM of 1942 and 1940 is associative
LCM of 1940 and 1942 = LCM of 1942 and 1940
1. What is the LCM of 1940 and 1942?
Answer: LCM of 1940 and 1942 is 1883740.
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 1942?
Answer: Factors of 1942 are 1, 2, 971, 1942. There are 4 integers that are factors of 1942. The greatest factor of 1942 is 1942.
4. How to Find the LCM of 1940 and 1942?
Answer:
Least Common Multiple of 1940 and 1942 = 1883740
Step 1: Find the prime factorization of 1940
1940 = 2 x 2 x 5 x 97
Step 2: Find the prime factorization of 1942
1942 = 2 x 971
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1883740 = 2 x 2 x 5 x 97 x 971
Step 4: Therefore, the least common multiple of 1940 and 1942 is 1883740.