Least Common Multiple (LCM) of 109 and 156
The least common multiple (LCM) of 109 and 156 is 17004.
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 156?
First, calculate the GCD of 109 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 156 = 0 remainder 109 |
| 2 | 156 ÷ 109 = 1 remainder 47 |
| 3 | 109 ÷ 47 = 2 remainder 15 |
| 4 | 47 ÷ 15 = 3 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 58 | 4350 |
| 14 and 68 | 476 |
| 103 and 133 | 13699 |
| 137 and 148 | 20276 |
| 35 and 77 | 385 |