Least Common Multiple (LCM) of 106 and 152
The least common multiple (LCM) of 106 and 152 is 8056.
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 106 and 152?
First, calculate the GCD of 106 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 152 = 0 remainder 106 |
| 2 | 152 ÷ 106 = 1 remainder 46 |
| 3 | 106 ÷ 46 = 2 remainder 14 |
| 4 | 46 ÷ 14 = 3 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 180 | 1980 |
| 175 and 170 | 5950 |
| 185 and 104 | 19240 |
| 103 and 78 | 8034 |
| 196 and 63 | 1764 |