Methods for finding the least common multiple are the prime factorization method and the rolling division method.

1, the decomposition of prime factors method: first of all, the minimum common multiple of the two numbers are required to prime factorization, to find all the prime factors, and listed, and then all the prime numbers in order from the largest to the smallest order listed, and finally arranged all the primes of the product, the minimum common multiple of the two numbers.

For example, to find the least common multiple of 100 and 45: 100=2×2×5×5, 45=3×3×5, combine the 2×2×5×5, 3×3×5 and order them in the same way, and finally you get 2250. so, the least common multiple of 100 and 45 is 2250.

2, Rollover division: also known as Euclid's algorithm, is an easy way to find the greatest common divisor of two positive integers. First of all, the larger of the two numbers divided by the smaller number, get the quotient and the remainder, and then the divisor into the original divisor, the remainder into the original divisor, and then divide, until the remainder is 0. Finally, at this point the divisor is the greatest common divisor of the original two numbers.

For example, to find the greatest common divisor of 126 and 84: divide the larger number 126 by the smaller number 84, and you get a quotient of 1 and a remainder of 42. We turn the divisor 84 into the original divisor 126, and the remainder 42 into the original divisor 84, and then we divide in the same way.

That is, 126 is divided by 84, and we get quotient 1 and remainder 42. 84 becomes the divisor, 42 becomes the divisor, and we continue to divide, and we get quotient 2 and remainder 0. At this point, the remainder is 0, so the greatest common divisor of 84 and 126 is 42.

Advantages of the rolling over method of division

Rolling over division is a simple and practical way of calculating the number of divisors in the same way. simple, practical, widely applicable, and fast calculation method. Its advantages include being easy to learn, easy to understand, suitable for solving multiple numbers, can be used for various operations such as fraction simplification, and is also faster and suitable for use in a variety of scientific calculations.