Least Common Multiple (LCM) of 105 and 152
The least common multiple (LCM) of 105 and 152 is 15960.
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 152?
First, calculate the GCD of 105 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 152 = 0 remainder 105 |
| 2 | 152 ÷ 105 = 1 remainder 47 |
| 3 | 105 ÷ 47 = 2 remainder 11 |
| 4 | 47 ÷ 11 = 4 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 101 | 10706 |
| 192 and 82 | 7872 |
| 92 and 198 | 9108 |
| 67 and 69 | 4623 |
| 18 and 200 | 1800 |