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 |
|---|---|
| 141 and 53 | 7473 |
| 70 and 73 | 5110 |
| 110 and 127 | 13970 |
| 106 and 163 | 17278 |
| 115 and 154 | 17710 |