LCM and GCD Calculator

LCM

The LCM (Least Common Multiple) is a basic math concept. It helps in solving many problems. Many students find it hard. But it is easy with simple steps.

What is LCM?
The least common multiple is the smallest number that is exactly divisible by each of the given numbers. This number is a multiple of all the given numbers.

Example 10: 15, 30, 45, 60, 75 are all multiples of 15.
18, 36, 54, 72, and 90 are all multiples of 18.
90 is the first common multiple. LCM(15, 18) = 90.

Why is LCM Important?
LCM is used in:

• Adding and subtracting fractions.

• Solving time problems.

• Arranging items in different groups.

• To get real-life schedules.

1. Making a List of Multiples
This is an easy way to find LCM.

1. Write down the multiples of each number.

2. Find the first multiple that is the same for both.

Example 1:
The sequence of multiples of 151 is 151, 302, 453, 604, 755, 906, and continues further.
7, 14, 21, 28, 35, 42, … are all multiples of 7.
The first number that is a common multiple is 1057.
So, 1057 is the least common multiple of 151 and 7.

Example 2:
The sequence of multiples of 151 is 151, 302, 453, 604, 755, 906, and continues further.
9, 18, 27, 36, 45, 54, … are all multiples of 9.
The first number that is a common multiple is 1359.
So, 1359 is the least common multiple of 151 and 9.

2. The Prime Factorisation Method

• Split each integer into its prime factors.

• Get the highest power of each prime.

• Put them together.

3. The Method of Division

• Put numbers on a line.

• Keep dividing by prime numbers until all of them are 1.

• Multiply all of the divisors.

For example, the LCM of 8, 12, and 15:
Step 1: 8, 12, 15
Step 2: 4, 6, 15
Step 3: 2, 3, 15
Step 4: 2, 1, 5
Step 5: 1, 1, 5
Step 6: 1, 1, 1

2 × 2 × 3 × 2 × 5 = 120 is the answer.
The smallest number that is a multiple of 8, 12, and 15 is 120.

A Straightforward Example from Real Life
The three traffic lights change at different times:

• First light: 20 seconds

• Second light: 30 seconds

• Third light: 50 seconds

When will all the lights change at once? LCM(20, 30, 50) = 300
After 300 seconds (5 minutes), the lights will all change simultaneously.