Least Common Multiple (LCM) of 156 and 99
The least common multiple (LCM) of 156 and 99 is 5148.
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 156 and 99?
First, calculate the GCD of 156 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 99 = 1 remainder 57 |
| 2 | 99 ÷ 57 = 1 remainder 42 |
| 3 | 57 ÷ 42 = 1 remainder 15 |
| 4 | 42 ÷ 15 = 2 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 17 | 595 |
| 92 and 108 | 2484 |
| 110 and 152 | 8360 |
| 120 and 15 | 120 |
| 14 and 122 | 854 |