Least Common Multiple (LCM) of 120 and 133
The least common multiple (LCM) of 120 and 133 is 15960.
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 133?
First, calculate the GCD of 120 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 133 = 0 remainder 120 |
| 2 | 133 ÷ 120 = 1 remainder 13 |
| 3 | 120 ÷ 13 = 9 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 61 | 11956 |
| 122 and 63 | 7686 |
| 132 and 169 | 22308 |
| 198 and 183 | 12078 |
| 33 and 102 | 1122 |