Least Common Multiple (LCM) of 120 and 163
The least common multiple (LCM) of 120 and 163 is 19560.
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 163?
First, calculate the GCD of 120 and 163 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 163 = 0 remainder 120 |
| 2 | 163 ÷ 120 = 1 remainder 43 |
| 3 | 120 ÷ 43 = 2 remainder 34 |
| 4 | 43 ÷ 34 = 1 remainder 9 |
| 5 | 34 ÷ 9 = 3 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 76 | 2204 |
| 151 and 162 | 24462 |
| 181 and 40 | 7240 |
| 155 and 162 | 25110 |
| 189 and 64 | 12096 |