Least Common Multiple (LCM) of 144 and 106
The least common multiple (LCM) of 144 and 106 is 7632.
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 144 and 106?
First, calculate the GCD of 144 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 106 = 1 remainder 38 |
| 2 | 106 ÷ 38 = 2 remainder 30 |
| 3 | 38 ÷ 30 = 1 remainder 8 |
| 4 | 30 ÷ 8 = 3 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 99 | 9999 |
| 74 and 144 | 5328 |
| 157 and 109 | 17113 |
| 182 and 108 | 9828 |
| 185 and 106 | 19610 |