Least Common Multiple (LCM) of 120 and 182
The least common multiple (LCM) of 120 and 182 is 10920.
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 182?
First, calculate the GCD of 120 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 182 = 0 remainder 120 |
| 2 | 182 ÷ 120 = 1 remainder 62 |
| 3 | 120 ÷ 62 = 1 remainder 58 |
| 4 | 62 ÷ 58 = 1 remainder 4 |
| 5 | 58 ÷ 4 = 14 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 124 | 21700 |
| 122 and 139 | 16958 |
| 134 and 98 | 6566 |
| 36 and 75 | 900 |
| 107 and 101 | 10807 |