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Solution - Least common multiple (LCM) by prime factorization

2,880
2,880

Step-by-step explanation

1. Find the prime factors of 48

Tree view of the prime factors of 48: 2, 2, 2, 2 and 3

The prime factors of 48 are 2, 2, 2, 2 and 3.

2. Find the prime factors of 64

Tree view of the prime factors of 64: 2, 2, 2, 2, 2 and 2

The prime factors of 64 are 2, 2, 2, 2, 2 and 2.

3. Find the prime factors of 90

Tree view of the prime factors of 90: 2, 3, 3 and 5

The prime factors of 90 are 2, 3, 3 and 5.

4. Find the prime factors of 120

Tree view of the prime factors of 120: 2, 2, 2, 3 and 5

The prime factors of 120 are 2, 2, 2, 3 and 5.

5. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5) occurs in the factorization of the given numbers:

Prime factorNumber48 64 90 120 Max. occurrence
246136
310212
500111

The prime factor 5 occurs one time, while 2 and 3 occur more than once.

6. Calculate the LCM

The least common multiple is the product of all factors in the greatest number of their occurrence.

LCM = 222222335

LCM = 26325

LCM = 2,880

The least common multiple of 48, 64, 90 and 120 is 2,880.

Why learn this

The least common multiple (LCM), sometimes called the lowest common multiple or least common divisor, is helpful for understanding the relationships between numbers. For example, if it takes Earth 365 days to orbit the sun and it takes Venus 225 days to orbit the sun and both are in perfect alignment at the time this scenario is given, how long will it take for Earth and Venus to align again? We can use LCM to determine that the answer would be 16,425 days.

LCM is also a very important part of many mathematical concepts that also have real-world applications. For example, we use LCMs when adding and subtracting fractions, which we use quite frequently.