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 |
|---|---|
| 69 and 199 | 13731 |
| 23 and 33 | 759 |
| 168 and 53 | 8904 |
| 83 and 69 | 5727 |
| 125 and 178 | 22250 |