Least Common Multiple (LCM) of 113 and 153
The least common multiple (LCM) of 113 and 153 is 17289.
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 113 and 153?
First, calculate the GCD of 113 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 153 = 0 remainder 113 |
| 2 | 153 ÷ 113 = 1 remainder 40 |
| 3 | 113 ÷ 40 = 2 remainder 33 |
| 4 | 40 ÷ 33 = 1 remainder 7 |
| 5 | 33 ÷ 7 = 4 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 75 | 2700 |
| 84 and 21 | 84 |
| 197 and 152 | 29944 |
| 118 and 18 | 1062 |
| 159 and 140 | 22260 |