Least Common Multiple (LCM) of 105 and 120
The least common multiple (LCM) of 105 and 120 is 840.
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 105 and 120?
First, calculate the GCD of 105 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 120 = 0 remainder 105 |
| 2 | 120 ÷ 105 = 1 remainder 15 |
| 3 | 105 ÷ 15 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 90 | 540 |
| 72 and 134 | 4824 |
| 149 and 38 | 5662 |
| 74 and 48 | 1776 |
| 83 and 123 | 10209 |