
Least Common Multiple (LCM) of 193 and 106
The least common multiple (LCM) of 193 and 106 is 20458.
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 193 and 106?
First, calculate the GCD of 193 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 193 ÷ 106 = 1 remainder 87 |
2 | 106 ÷ 87 = 1 remainder 19 |
3 | 87 ÷ 19 = 4 remainder 11 |
4 | 19 ÷ 11 = 1 remainder 8 |
5 | 11 ÷ 8 = 1 remainder 3 |
6 | 8 ÷ 3 = 2 remainder 2 |
7 | 3 ÷ 2 = 1 remainder 1 |
8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
200 and 117 | 23400 |
87 and 164 | 14268 |
106 and 14 | 742 |
161 and 49 | 1127 |
188 and 141 | 564 |