Least Common Multiple (LCM) of 153 and 120
The least common multiple (LCM) of 153 and 120 is 6120.
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 153 and 120?
First, calculate the GCD of 153 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 120 = 1 remainder 33 |
| 2 | 120 ÷ 33 = 3 remainder 21 |
| 3 | 33 ÷ 21 = 1 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 184 | 16008 |
| 43 and 14 | 602 |
| 125 and 144 | 18000 |
| 21 and 175 | 525 |
| 154 and 106 | 8162 |