Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1960 and 1966 the smallest integer that is 1926680 that is divisible by both numbers.
Least Common Multiple (LCM) of 1960 and 1966 is 1926680.
LCM(1960,1966) = 1926680
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 1960 and 1966. First we will calculate the prime factors of 1960 and 1966.
Prime Factorization of 1960
2 | 1960 |
2 | 980 |
2 | 490 |
5 | 245 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 1960 are 2, 5,7. Prime factorization of 1960 in exponential form is:
1960 = 23×51×72
Prime Factorization of 1966
2 | 1966 |
983 | 983 |
1 |
Prime factors of 1966 are 2,983. Prime factorization of 1966 in exponential form is:
1966 = 21×9831
Now multiplying the highest exponent prime factors to calculate the LCM of 1960 and 1966.
LCM(1960,1966) = 23×51×72×9831
LCM(1960,1966) = 1926680
Factors of 1960
List of positive integer factors of 1960 that divides 1960 without a remainder.
1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960
Factors of 1966
List of positive integer factors of 1966 that divides 1966 without a remainder.
1, 2, 983, 1966
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1960 and 1966, than apply into the LCM equation.
GCF(1960,1966) = 2
LCM(1960,1966) = ( 1960 × 1966) / 2
LCM(1960,1966) = 3853360 / 2
LCM(1960,1966) = 1926680
(i) The LCM of 1966 and 1960 is associative
LCM of 1960 and 1966 = LCM of 1966 and 1960
1. What is the LCM of 1960 and 1966?
Answer: LCM of 1960 and 1966 is 1926680.
2. What are the Factors of 1960?
Answer: Factors of 1960 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960. There are 24 integers that are factors of 1960. The greatest factor of 1960 is 1960.
3. What are the Factors of 1966?
Answer: Factors of 1966 are 1, 2, 983, 1966. There are 4 integers that are factors of 1966. The greatest factor of 1966 is 1966.
4. How to Find the LCM of 1960 and 1966?
Answer:
Least Common Multiple of 1960 and 1966 = 1926680
Step 1: Find the prime factorization of 1960
1960 = 2 x 2 x 2 x 5 x 7 x 7
Step 2: Find the prime factorization of 1966
1966 = 2 x 983
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1926680 = 2 x 2 x 2 x 5 x 7 x 7 x 983
Step 4: Therefore, the least common multiple of 1960 and 1966 is 1926680.