Least Common Multiple (LCM) of 105 and 60
The least common multiple (LCM) of 105 and 60 is 420.
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 60?
First, calculate the GCD of 105 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 60 = 1 remainder 45 |
| 2 | 60 ÷ 45 = 1 remainder 15 |
| 3 | 45 ÷ 15 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 91 | 12012 |
| 106 and 124 | 6572 |
| 82 and 172 | 7052 |
| 193 and 198 | 38214 |
| 128 and 103 | 13184 |