Least Common Multiple (LCM) of 56 and 156
The least common multiple (LCM) of 56 and 156 is 2184.
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 56 and 156?
First, calculate the GCD of 56 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 156 = 0 remainder 56 |
| 2 | 156 ÷ 56 = 2 remainder 44 |
| 3 | 56 ÷ 44 = 1 remainder 12 |
| 4 | 44 ÷ 12 = 3 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 195 | 7995 |
| 159 and 64 | 10176 |
| 100 and 69 | 6900 |
| 184 and 125 | 23000 |
| 111 and 83 | 9213 |