Least Common Multiple (LCM) of 55 and 94
The least common multiple (LCM) of 55 and 94 is 5170.
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 55 and 94?
First, calculate the GCD of 55 and 94 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 94 = 0 remainder 55 |
| 2 | 94 ÷ 55 = 1 remainder 39 |
| 3 | 55 ÷ 39 = 1 remainder 16 |
| 4 | 39 ÷ 16 = 2 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 64 | 9792 |
| 96 and 59 | 5664 |
| 85 and 20 | 340 |
| 170 and 19 | 3230 |
| 153 and 56 | 8568 |