Least Common Multiple (LCM) of 120 and 193
The least common multiple (LCM) of 120 and 193 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 120 and 193?
First, calculate the GCD of 120 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 193 = 0 remainder 120 |
| 2 | 193 ÷ 120 = 1 remainder 73 |
| 3 | 120 ÷ 73 = 1 remainder 47 |
| 4 | 73 ÷ 47 = 1 remainder 26 |
| 5 | 47 ÷ 26 = 1 remainder 21 |
| 6 | 26 ÷ 21 = 1 remainder 5 |
| 7 | 21 ÷ 5 = 4 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 83 | 10790 |
| 156 and 95 | 14820 |
| 170 and 104 | 8840 |
| 193 and 45 | 8685 |
| 110 and 188 | 10340 |