
Least Common Multiple (LCM) of 97 and 107
The least common multiple (LCM) of 97 and 107 is 10379.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 97 and 107?
First, calculate the GCD of 97 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 97 ÷ 107 = 0 remainder 97 |
2 | 107 ÷ 97 = 1 remainder 10 |
3 | 97 ÷ 10 = 9 remainder 7 |
4 | 10 ÷ 7 = 1 remainder 3 |
5 | 7 ÷ 3 = 2 remainder 1 |
6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
137 and 81 | 11097 |
25 and 27 | 675 |
163 and 107 | 17441 |
102 and 33 | 1122 |
159 and 40 | 6360 |