Least Common Multiple (LCM) of 113 and 152
The least common multiple (LCM) of 113 and 152 is 17176.
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 152?
First, calculate the GCD of 113 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 152 = 0 remainder 113 |
| 2 | 152 ÷ 113 = 1 remainder 39 |
| 3 | 113 ÷ 39 = 2 remainder 35 |
| 4 | 39 ÷ 35 = 1 remainder 4 |
| 5 | 35 ÷ 4 = 8 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 119 | 3808 |
| 200 and 71 | 14200 |
| 172 and 158 | 13588 |
| 117 and 114 | 4446 |
| 30 and 53 | 1590 |