Least common multiple of 30 and 40, least common multiple of 30 and 45?

It's 120.

Least common multiple = 2 * 5 * 3 * 2 * 2 = 120 (because 30 and 40 both have 2*5, so 2*5 is only multiplied once.) ）

Least common multiple concept:

The smallest of the common multiples of two or more integers is called their least common multiple.

Calculation method: 1) Decomposition prime factor method.

Write out the prime factors of these numbers first, and the least common multiple is equal to the product of all their prime factors (if there are several prime factors that are the same, compare which of the two numbers has the more prime factors and multiplies more times).

For example, find the least common multiple of 45 and 30.

The different prime factors are 2 and 3, which are the prime factors that they both have, and since 45 has two 3s and 30 has only one 3, multiply two 3s when calculating the least common multiple

The least common multiple is equal to 2*3*3*5=90

Another example is calculating the least common multiple of 36 and 270.

The different prime factors are that this prime factor is more in 36, which is two, so multiply it twice; The prime factor of 3 is more than 270, which is three, so it is multiplied by three times.

The least common multiple is equal to 2*2*3*3*3*5=540

The least common multiple of 20 and 40 is 40

2) Formula method.

Since the product of two numbers is equal to the product of the greatest common divisor and the least common multiple of these two numbers. i.e. (a,b) [a,b]=a b. So, to find the least common multiple of two numbers, you can first find their greatest common divisor, and then use the above formula to find their least common multiple.

For example, if you find [18,20], you get [18,20]=18 20 (18,20)=18 20 2=180. To find the least common multiple of several natural numbers, you can first find the least common multiple of two of the numbers, and then find the least common multiple of this least common multiple and the least common multiple of the third number, and then continue until the last one. The resulting least common multiple is the least common multiple of the numbers sought. [4]

120, I pledge with my life! I'm a 5th grader !!

Method: Short division. The process is as follows:

The least common multiple of the two of them is 90

Take a look at the short division on the graph below.

Therefore, the minimum multiplier of the hole in the socks is:

Solve the problem of least common multiples.

Because 30 = 2 3 5

So their least common multiple is 2 5 2 2 3 3 = 360

So their least common multiple is 360

Decomposed into prime factors: 45 = 3 3 530 = 2 3 520 = 2 2 5 greatest common divisor = multiplication of repeated prime factors There is only one prime factor 5 with careful convincing, so the bridge method of the greatest common divisor is 5 The bridge method of the least common multiple of 5 is the factor width elimination wheel multiplication, and the repeated prime factor is multiplied only once The prime factors of 45 and 30 contain , cause.