Least Common Multiple (LCM) of 120 and 143
The least common multiple (LCM) of 120 and 143 is 17160.
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 143?
First, calculate the GCD of 120 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 143 = 0 remainder 120 |
| 2 | 143 ÷ 120 = 1 remainder 23 |
| 3 | 120 ÷ 23 = 5 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 124 | 4092 |
| 97 and 172 | 16684 |
| 189 and 73 | 13797 |
| 56 and 179 | 10024 |
| 82 and 160 | 6560 |