Least Common Multiple (LCM) of 120 and 156
The least common multiple (LCM) of 120 and 156 is 1560.
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 120 and 156?
First, calculate the GCD of 120 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 156 = 0 remainder 120 |
| 2 | 156 ÷ 120 = 1 remainder 36 |
| 3 | 120 ÷ 36 = 3 remainder 12 |
| 4 | 36 ÷ 12 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 87 | 8787 |
| 45 and 162 | 810 |
| 135 and 187 | 25245 |
| 189 and 30 | 1890 |
| 167 and 30 | 5010 |