Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1963 and 1968 the smallest integer that is 3863184 that is divisible by both numbers.
Least Common Multiple (LCM) of 1963 and 1968 is 3863184.
LCM(1963,1968) = 3863184
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 1963 and 1968. First we will calculate the prime factors of 1963 and 1968.
Prime Factorization of 1963
13 | 1963 |
151 | 151 |
1 |
Prime factors of 1963 are 13,151. Prime factorization of 1963 in exponential form is:
1963 = 131×1511
Prime Factorization of 1968
2 | 1968 |
2 | 984 |
2 | 492 |
2 | 246 |
3 | 123 |
41 | 41 |
1 |
Prime factors of 1968 are 2, 3,41. Prime factorization of 1968 in exponential form is:
1968 = 24×31×411
Now multiplying the highest exponent prime factors to calculate the LCM of 1963 and 1968.
LCM(1963,1968) = 24×31×131×411×1511
LCM(1963,1968) = 3863184
Factors of 1963
List of positive integer factors of 1963 that divides 1963 without a remainder.
1, 13, 151, 1963
Factors of 1968
List of positive integer factors of 1968 that divides 1968 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1963 and 1968, than apply into the LCM equation.
GCF(1963,1968) = 1
LCM(1963,1968) = ( 1963 × 1968) / 1
LCM(1963,1968) = 3863184 / 1
LCM(1963,1968) = 3863184
(i) The LCM of 1968 and 1963 is associative
LCM of 1963 and 1968 = LCM of 1968 and 1963
1. What is the LCM of 1963 and 1968?
Answer: LCM of 1963 and 1968 is 3863184.
2. What are the Factors of 1963?
Answer: Factors of 1963 are 1, 13, 151, 1963. There are 4 integers that are factors of 1963. The greatest factor of 1963 is 1963.
3. What are the Factors of 1968?
Answer: Factors of 1968 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 41, 48, 82, 123, 164, 246, 328, 492, 656, 984, 1968. There are 20 integers that are factors of 1968. The greatest factor of 1968 is 1968.
4. How to Find the LCM of 1963 and 1968?
Answer:
Least Common Multiple of 1963 and 1968 = 3863184
Step 1: Find the prime factorization of 1963
1963 = 13 x 151
Step 2: Find the prime factorization of 1968
1968 = 2 x 2 x 2 x 2 x 3 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3863184 = 2 x 2 x 2 x 2 x 3 x 13 x 41 x 151
Step 4: Therefore, the least common multiple of 1963 and 1968 is 3863184.