Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 7738 and 7746 the smallest integer that is 29969274 that is divisible by both numbers.
Least Common Multiple (LCM) of 7738 and 7746 is 29969274.
LCM(7738,7746) = 29969274
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 7738 and 7746. First we will calculate the prime factors of 7738 and 7746.
Prime Factorization of 7738
2 | 7738 |
53 | 3869 |
73 | 73 |
1 |
Prime factors of 7738 are 2, 53,73. Prime factorization of 7738 in exponential form is:
7738 = 21×531×731
Prime Factorization of 7746
2 | 7746 |
3 | 3873 |
1291 | 1291 |
1 |
Prime factors of 7746 are 2, 3,1291. Prime factorization of 7746 in exponential form is:
7746 = 21×31×12911
Now multiplying the highest exponent prime factors to calculate the LCM of 7738 and 7746.
LCM(7738,7746) = 21×31×531×731×12911
LCM(7738,7746) = 29969274
Factors of 7738
List of positive integer factors of 7738 that divides 7738 without a remainder.
1, 2, 53, 73, 106, 146, 3869, 7738
Factors of 7746
List of positive integer factors of 7746 that divides 7746 without a remainder.
1, 2, 3, 6, 1291, 2582, 3873, 7746
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7738 and 7746, than apply into the LCM equation.
GCF(7738,7746) = 2
LCM(7738,7746) = ( 7738 × 7746) / 2
LCM(7738,7746) = 59938548 / 2
LCM(7738,7746) = 29969274
(i) The LCM of 7746 and 7738 is associative
LCM of 7738 and 7746 = LCM of 7746 and 7738
1. What is the LCM of 7738 and 7746?
Answer: LCM of 7738 and 7746 is 29969274.
2. What are the Factors of 7738?
Answer: Factors of 7738 are 1, 2, 53, 73, 106, 146, 3869, 7738. There are 8 integers that are factors of 7738. The greatest factor of 7738 is 7738.
3. What are the Factors of 7746?
Answer: Factors of 7746 are 1, 2, 3, 6, 1291, 2582, 3873, 7746. There are 8 integers that are factors of 7746. The greatest factor of 7746 is 7746.
4. How to Find the LCM of 7738 and 7746?
Answer:
Least Common Multiple of 7738 and 7746 = 29969274
Step 1: Find the prime factorization of 7738
7738 = 2 x 53 x 73
Step 2: Find the prime factorization of 7746
7746 = 2 x 3 x 1291
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 29969274 = 2 x 3 x 53 x 73 x 1291
Step 4: Therefore, the least common multiple of 7738 and 7746 is 29969274.