Least Common Multiple (LCM) of 55 and 152
The least common multiple (LCM) of 55 and 152 is 8360.
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 152?
First, calculate the GCD of 55 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 152 = 0 remainder 55 |
| 2 | 152 ÷ 55 = 2 remainder 42 |
| 3 | 55 ÷ 42 = 1 remainder 13 |
| 4 | 42 ÷ 13 = 3 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 30 | 870 |
| 23 and 179 | 4117 |
| 54 and 41 | 2214 |
| 51 and 167 | 8517 |
| 169 and 100 | 16900 |