Least Common Multiple (LCM) of 152 and 105
The least common multiple (LCM) of 152 and 105 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 152 and 105?
First, calculate the GCD of 152 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 105 = 1 remainder 47 |
| 2 | 105 ÷ 47 = 2 remainder 11 |
| 3 | 47 ÷ 11 = 4 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 46 | 1104 |
| 200 and 135 | 5400 |
| 97 and 22 | 2134 |
| 167 and 54 | 9018 |
| 37 and 171 | 6327 |