Ans: The concept of LCM has important use in real life like such as in solving problems related to racetracks, traffic lights, etc. Why do we use HCF? Ans: HCF is used to calculate the largest size of tile, the largest tape to measure the land, the maximum scale to measure length etc. Learn About Common Factors. If you have any queries regarding this article, reach out to us through the comment section below and we will get back to you as soon as possible.
Support: support embibe. General: info embibe. Algebra Formulas. Log Table. Geometry Formulas. Probability Formula. Arithmetic Progression Formulas. Make 36 as the divisor and as the dividend and perform the division again. Here the obtained remainder is Make 18 as the divisor and 36 as the dividend and perform the division again.
Here the obtained remainder is 0. Lets us find the LCM of and by division method using the following steps:. Example 3: Find the HCF of , using the division method. Solution: To find the HCF of and by the division method, we will follow the given steps:. Example 4. Solution: To find the HCF of , and by prime factorization method let us first do the prime factorization of the three numbers. The least common multiple LCM of two or more numbers is the smallest number among all the common multiples of the given numbers, whereas, the HCF Highest Common Factor of two or more numbers is the highest number among all the common factors of the given numbers.
Let us assume 'a' and 'b' are the two given numbers. For example, let us take two numbers 12 and 8. The two common ways to find the HCF and LCM of the given numbers are the prime factorization method and the division method.
Here, the common prime factors between the two numbers are: 2 and 5. Now, l et us find the LCM of 50 and 80 using prime factorization. Learn Practice Download. Solution: First, we will find the HCF of the two numbers and using the given steps: Divide by Solution : The required number leaves remainders 1 and 4 on dividing 70 and 50 respectively.
This means that the number exactly divides 69 and So, we need to find the HCF of 69 3 x 23 and 46 2 x Question 4 : Find the largest number which divides 64, and to leave the same remainder in each case.
Solution : To find the required number, we need to find the HCF of , and , i. Question 5 : Find the least number which when divided by 5,7,9 and 12, leaves the same remainder 3 in each case Solution : In these type of questions, we need to find the LCM of the divisors and add the common remainder 3 to it.
Solution : The largest four digit number is If they all blow the whistle simultaneously at hours, then at what time do they whistle again together? Solution : They all will whistle again at the same time after an interval that is equal to the LCM of their individual whistle blowing cycles.
Question 8 : Find the least number which when divided by 6,7,8 leaves a remainder 3, but when divided by 9 leaves no remainder. We know that a number is divisible by 9 if the sum of its digits is a multiple of 9. Therefore, the required number is Question 9 : Two numbers are in the ratio So, the numbers are 2m and 3m.
Question 10 : A rectangular field of dimension m x m is to be paved by identical square tiles. Find the size of each tile and the number of tiles required. Solution : We need to find the size of a square tile such that a number of tiles cover the field exactly, leaving no area unpaved.
For this, we find the HCF of the length and breadth of the field. Factorization Method. Prime Factorization Method. Division Method. In the hcf by factorization method,we find the greatest common factor by listing down the factors of the numbers.
Step 1: List down the factors of all the given numbers. Step 2: Look for the highest factor among the listed factors which are common for both the given numbers. Let us take an example:. Problem :Find the H. Since, the highest common factor of 36 and 45 is 9, therefore H. Let us consider an example,. Step 1: In calculating the hcf by prime factorization, we factorize the numbers into prime numbers, which is known as the prime factors.
Step 3: Finally, then write the numbers as a product of the prime numbers. The product of these common factors is the highest common factor of the given numbers. Find the hcf by prime factorization of the numbers 24 and Solution: To find the hcf by prime factorization ,.
0コメント