Least Common Multiple (LCM) of 156 and 113
The least common multiple (LCM) of 156 and 113 is 17628.
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 156 and 113?
First, calculate the GCD of 156 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 113 = 1 remainder 43 |
| 2 | 113 ÷ 43 = 2 remainder 27 |
| 3 | 43 ÷ 27 = 1 remainder 16 |
| 4 | 27 ÷ 16 = 1 remainder 11 |
| 5 | 16 ÷ 11 = 1 remainder 5 |
| 6 | 11 ÷ 5 = 2 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 49 | 1470 |
| 153 and 193 | 29529 |
| 83 and 84 | 6972 |
| 158 and 127 | 20066 |
| 84 and 13 | 1092 |