Least Common Multiple (LCM) of 109 and 48
The least common multiple (LCM) of 109 and 48 is 5232.
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 109 and 48?
First, calculate the GCD of 109 and 48 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 48 = 2 remainder 13 |
| 2 | 48 ÷ 13 = 3 remainder 9 |
| 3 | 13 ÷ 9 = 1 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 18 | 90 |
| 139 and 195 | 27105 |
| 22 and 147 | 3234 |
| 70 and 147 | 1470 |
| 106 and 195 | 20670 |