Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1944 and 1946 the smallest integer that is 1891512 that is divisible by both numbers.
Least Common Multiple (LCM) of 1944 and 1946 is 1891512.
LCM(1944,1946) = 1891512
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 1944 and 1946. First we will calculate the prime factors of 1944 and 1946.
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
Prime Factorization of 1946
2 | 1946 |
7 | 973 |
139 | 139 |
1 |
Prime factors of 1946 are 2, 7,139. Prime factorization of 1946 in exponential form is:
1946 = 21×71×1391
Now multiplying the highest exponent prime factors to calculate the LCM of 1944 and 1946.
LCM(1944,1946) = 23×35×71×1391
LCM(1944,1946) = 1891512
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
Factors of 1946
List of positive integer factors of 1946 that divides 1946 without a remainder.
1, 2, 7, 14, 139, 278, 973, 1946
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1944 and 1946, than apply into the LCM equation.
GCF(1944,1946) = 2
LCM(1944,1946) = ( 1944 × 1946) / 2
LCM(1944,1946) = 3783024 / 2
LCM(1944,1946) = 1891512
(i) The LCM of 1946 and 1944 is associative
LCM of 1944 and 1946 = LCM of 1946 and 1944
1. What is the LCM of 1944 and 1946?
Answer: LCM of 1944 and 1946 is 1891512.
2. 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.
3. What are the Factors of 1946?
Answer: Factors of 1946 are 1, 2, 7, 14, 139, 278, 973, 1946. There are 8 integers that are factors of 1946. The greatest factor of 1946 is 1946.
4. How to Find the LCM of 1944 and 1946?
Answer:
Least Common Multiple of 1944 and 1946 = 1891512
Step 1: Find the prime factorization of 1944
1944 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 1946
1946 = 2 x 7 x 139
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1891512 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 7 x 139
Step 4: Therefore, the least common multiple of 1944 and 1946 is 1891512.