We need to find the least common multiple of 5 and 7. The least common multiple, referred to as LCM (least common multiple), is the smallest positive integer multiple of two or more integers, which can be divisible by these integers without leaving a remainder.
In order to find the least common multiple of 5 and 7, we can use a method called "prime factorization". Prime factorization is to represent a number as the product of a series of prime numbers. For example, 10 can be decomposed into 2×5. For 5 and 7, they are already prime numbers, so their prime factorization is themselves.
After finding the prime factorization of two numbers, in order to get their least common multiple, we need to take the highest power of each prime factor and multiply it.
It is expressed by mathematical formula: LCM(a, b) = p 1 max (m 1, n 1) × p2 max (m2, N2)× 1...× pk max (mk, nk), where p/kloc.
For 5 and 7, because they are both prime numbers, their prime factorization is their own, and their exponents are 1. Therefore, LCM (5 5,7) = 5max (1,1) × 7 max (0,1) = 5x7. The calculation result is: LCM (5 5,7) = 35, so the least common multiple of 5 and 7 is: 35.
Methods to solve mathematical problems:
1. Algebraic method: solving problems by establishing algebraic expressions or equations. For example, in geometric problems, it is often necessary to establish equations to express angles, lengths and so on. , and then solved by algebraic operation.
2. Number-shape combination method: the number relationship in mathematical problems is combined with geometric figures, and the problem is understood through intuitive figures. For example, when solving geometry problems, it is often necessary to draw a figure, and then look for clues to solve the problem by observing the figure.
3. Induction: By observing and summarizing a series of concrete examples, we can draw a general conclusion. For example, when solving the sequence problem, we can summarize the general term formula of the sequence by observing the first few terms of the sequence.
4. Reduction to absurdity: By denying the conclusion of the question, and then gradually deducing, contradictions are found, thus proving the correctness of the original conclusion. For example, when proving a mathematical proposition, the hypothesis is often not established first, and then the contradiction is deduced, thus proving the correctness of the original proposition.
5. Construction method: according to the conditions and conclusions of the topic, construct a qualified mathematical object or model. For example, when solving inequality problems, we can solve the problem by constructing auxiliary functions.