Least Common Multiple (LCM) of 116 and 153
The least common multiple (LCM) of 116 and 153 is 17748.
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 116 and 153?
First, calculate the GCD of 116 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 153 = 0 remainder 116 |
| 2 | 153 ÷ 116 = 1 remainder 37 |
| 3 | 116 ÷ 37 = 3 remainder 5 |
| 4 | 37 ÷ 5 = 7 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 152 | 2280 |
| 52 and 55 | 2860 |
| 34 and 92 | 1564 |
| 25 and 34 | 850 |
| 197 and 181 | 35657 |