Least Common Multiple (LCM) of 105 and 156
The least common multiple (LCM) of 105 and 156 is 5460.
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 156?
First, calculate the GCD of 105 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 156 = 0 remainder 105 |
| 2 | 156 ÷ 105 = 1 remainder 51 |
| 3 | 105 ÷ 51 = 2 remainder 3 |
| 4 | 51 ÷ 3 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 195 | 4485 |
| 192 and 172 | 8256 |
| 146 and 141 | 20586 |
| 139 and 47 | 6533 |
| 156 and 15 | 780 |