Least Common Multiple (LCM) of 152 and 111
The least common multiple (LCM) of 152 and 111 is 16872.
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 152 and 111?
First, calculate the GCD of 152 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 111 = 1 remainder 41 |
| 2 | 111 ÷ 41 = 2 remainder 29 |
| 3 | 41 ÷ 29 = 1 remainder 12 |
| 4 | 29 ÷ 12 = 2 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 145 | 21460 |
| 55 and 148 | 8140 |
| 49 and 40 | 1960 |
| 12 and 103 | 1236 |
| 87 and 196 | 17052 |