Least Common Multiple (LCM) of 56 and 84
The least common multiple (LCM) of 56 and 84 is 168.
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 84?
First, calculate the GCD of 56 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 56 ÷ 84 = 0 remainder 56 |
| 2 | 84 ÷ 56 = 1 remainder 28 |
| 3 | 56 ÷ 28 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 178 | 33642 |
| 72 and 34 | 1224 |
| 147 and 111 | 5439 |
| 141 and 161 | 22701 |
| 31 and 162 | 5022 |