Least Common Multiple (LCM) of 60 and 156
The least common multiple (LCM) of 60 and 156 is 780.
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 60 and 156?
First, calculate the GCD of 60 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 156 = 0 remainder 60 |
| 2 | 156 ÷ 60 = 2 remainder 36 |
| 3 | 60 ÷ 36 = 1 remainder 24 |
| 4 | 36 ÷ 24 = 1 remainder 12 |
| 5 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 199 | 35820 |
| 132 and 21 | 924 |
| 70 and 75 | 1050 |
| 74 and 192 | 7104 |
| 135 and 119 | 16065 |