Least Common Multiple (LCM) of 55 and 32
The least common multiple (LCM) of 55 and 32 is 1760.
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 32?
First, calculate the GCD of 55 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 32 = 1 remainder 23 |
| 2 | 32 ÷ 23 = 1 remainder 9 |
| 3 | 23 ÷ 9 = 2 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 135 | 7155 |
| 66 and 112 | 3696 |
| 88 and 136 | 1496 |
| 166 and 139 | 23074 |
| 193 and 179 | 34547 |