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Finding the LCM Using the Prime Factors Method
The prime factors method is a systematic procedure for computing the least common multiple of two (or more) numbers by leveraging their prime factorizations. The steps are:
- Write each number as a product of primes using a factor tree or repeated division.
- List the prime factors of each number and align matching primes vertically — place identical primes in the same column so shared factors line up.
- Bring down one number from every column — each column contributes exactly one prime to the LCM, ensuring that common primes are counted only once while all distinct primes are included.
- Multiply the collected factors — the product is the LCM. Because matching common primes prevents any shared factor from being counted twice, this method guarantees the result is the least common multiple rather than just any common multiple.
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