Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1953 and 1954 the smallest integer that is 3816162 that is divisible by both numbers.
Least Common Multiple (LCM) of 1953 and 1954 is 3816162.
LCM(1953,1954) = 3816162
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 1953 and 1954. First we will calculate the prime factors of 1953 and 1954.
Prime Factorization of 1953
3 | 1953 |
3 | 651 |
7 | 217 |
31 | 31 |
1 |
Prime factors of 1953 are 3, 7,31. Prime factorization of 1953 in exponential form is:
1953 = 32×71×311
Prime Factorization of 1954
2 | 1954 |
977 | 977 |
1 |
Prime factors of 1954 are 2,977. Prime factorization of 1954 in exponential form is:
1954 = 21×9771
Now multiplying the highest exponent prime factors to calculate the LCM of 1953 and 1954.
LCM(1953,1954) = 21×32×71×311×9771
LCM(1953,1954) = 3816162
Factors of 1953
List of positive integer factors of 1953 that divides 1953 without a remainder.
1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953
Factors of 1954
List of positive integer factors of 1954 that divides 1954 without a remainder.
1, 2, 977, 1954
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1953 and 1954, than apply into the LCM equation.
GCF(1953,1954) = 1
LCM(1953,1954) = ( 1953 × 1954) / 1
LCM(1953,1954) = 3816162 / 1
LCM(1953,1954) = 3816162
(i) The LCM of 1954 and 1953 is associative
LCM of 1953 and 1954 = LCM of 1954 and 1953
1. What is the LCM of 1953 and 1954?
Answer: LCM of 1953 and 1954 is 3816162.
2. What are the Factors of 1953?
Answer: Factors of 1953 are 1, 3, 7, 9, 21, 31, 63, 93, 217, 279, 651, 1953. There are 12 integers that are factors of 1953. The greatest factor of 1953 is 1953.
3. What are the Factors of 1954?
Answer: Factors of 1954 are 1, 2, 977, 1954. There are 4 integers that are factors of 1954. The greatest factor of 1954 is 1954.
4. How to Find the LCM of 1953 and 1954?
Answer:
Least Common Multiple of 1953 and 1954 = 3816162
Step 1: Find the prime factorization of 1953
1953 = 3 x 3 x 7 x 31
Step 2: Find the prime factorization of 1954
1954 = 2 x 977
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3816162 = 2 x 3 x 3 x 7 x 31 x 977
Step 4: Therefore, the least common multiple of 1953 and 1954 is 3816162.