Least Common Multiple (LCM) of 193 and 120
The least common multiple (LCM) of 193 and 120 is 23160.
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 120?
First, calculate the GCD of 193 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 120 = 1 remainder 73 |
| 2 | 120 ÷ 73 = 1 remainder 47 |
| 3 | 73 ÷ 47 = 1 remainder 26 |
| 4 | 47 ÷ 26 = 1 remainder 21 |
| 5 | 26 ÷ 21 = 1 remainder 5 |
| 6 | 21 ÷ 5 = 4 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 31 | 3596 |
| 166 and 122 | 10126 |
| 137 and 157 | 21509 |
| 123 and 98 | 12054 |
| 25 and 160 | 800 |