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Solution - Least common multiple (LCM) by prime factorization

352,182,600
352,182,600

Step-by-step explanation

1. Find the prime factors of 2,772

Tree view of the prime factors of 2,772: 2, 2, 3, 3, 7 and 11

The prime factors of 2,772 are 2, 2, 3, 3, 7 and 11.

2. Find the prime factors of 52,920

Tree view of the prime factors of 52,920: 2, 2, 2, 3, 3, 3, 5, 7 and 7

The prime factors of 52,920 are 2, 2, 2, 3, 3, 3, 5, 7 and 7.

3. Find the prime factors of 1,397,550

Tree view of the prime factors of 1,397,550: 2, 3, 5, 5, 7, 11, 11 and 11

The prime factors of 1,397,550 are 2, 3, 5, 5, 7, 11, 11 and 11.

4. Build a prime factors table

Determine the maximum number of times each prime factor (2, 3, 5, 7, 11) occurs in the factorization of the given numbers:

Prime factorNumber2,77252,9201,397,550Max. occurrence
22313
32313
50122
71212
111033

The prime factors 2, 3, 5, 7 and 11 occur more than once.

5. Calculate the LCM

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

LCM = 2223335577111111

LCM = 23335272113

LCM = 352,182,600

The least common multiple of 2,772, 52,920 and 1,397,550 is 352,182,600.

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.