Least Common Multiple (LCM) of 153 and 59
The least common multiple (LCM) of 153 and 59 is 9027.
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 153 and 59?
First, calculate the GCD of 153 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 59 = 2 remainder 35 |
| 2 | 59 ÷ 35 = 1 remainder 24 |
| 3 | 35 ÷ 24 = 1 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 132 | 1188 |
| 45 and 200 | 1800 |
| 33 and 168 | 1848 |
| 198 and 109 | 21582 |
| 25 and 104 | 2600 |