Penyelesaian - Least common multiple (LCM) by prime factorization

Hasil Akhir Langkah-langkah Terma dan topik

96

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Penjelasan langkah demi langkah

1. Find the prime factors of 6

Tree view of the prime factors of 6: 2 and 3

The prime factors of 6 are 2 and 3.

2. Find the prime factors of 12

Tree view of the prime factors of 12: 2, 2 and 3

The prime factors of 12 are 2, 2 and 3.

3. Find the prime factors of 24

Tree view of the prime factors of 24: 2, 2, 2 and 3

The prime factors of 24 are 2, 2, 2 and 3.

4. 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.

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 factorNumber	6	12	24	32	Max. occurrence
2	1	2	3	5	5
3	1	1	1	0	1

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 = $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$

LCM = $2^{5} \cdot 3$

LCM = 96

The least common multiple of 6, 12, 24 and 32 is 96.

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Mengapa belajar ini

Learn more with Tiger

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.