Least Common Multiple (LCM) of 109 and 153
The least common multiple (LCM) of 109 and 153 is 16677.
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 153?
First, calculate the GCD of 109 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 153 = 0 remainder 109 |
| 2 | 153 ÷ 109 = 1 remainder 44 |
| 3 | 109 ÷ 44 = 2 remainder 21 |
| 4 | 44 ÷ 21 = 2 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 36 | 1548 |
| 144 and 29 | 4176 |
| 60 and 12 | 60 |
| 104 and 90 | 4680 |
| 16 and 180 | 720 |