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Solution - Least common multiple (LCM) by prime factorization

384
384

Step-by-step explanation

1. Find the prime factors of 32

Tree view of the prime factors of 32: 2, 2, 2, 2 and 2

The prime factors of 32 are 2, 2, 2, 2 and 2.

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 96

Tree view of the prime factors of 96: 2, 2, 2, 2, 2 and 3

The prime factors of 96 are 2, 2, 2, 2, 2 and 3.

4. Find the prime factors of 128

Tree view of the prime factors of 128: 2, 2, 2, 2, 2, 2 and 2

The prime factors of 128 are 2, 2, 2, 2, 2, 2 and 2.

5. Build a prime factors table

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

Prime factorNumber32 64 96 128 Max. occurrence
256577
300101

The prime factor 3 occurs one time, while 2 occurs 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 = 22222223

LCM = 273

LCM = 384

The least common multiple of 32, 64, 96 and 128 is 384.

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.