How to find HCF and LCM

By multiplying all the factors in a list, the highest common factor is discovered.By multiplying all of the factors in a list, you can find the lowest common multiple.

A number can be expressed as a product of its prime factors by prime factorization. A prime number has only two factors: one and the number itself. Consider the number 30 as an example. Although 30 = 5× 6 is a prime number, 6 is not. The number 6 can also be factored as 2 ×3 (prime numbers 2 and 3). As a result, 30 has a prime factorization of 2× 3× 5 with all factors being prime numbers.

Let’s learn more about prime factorization by working through a variety of mathematics problems, which will be followed by solved examples and practice questions.

Meaning of Prime Factorization

Prime factorization is the technique of expressing a number as the sum of prime numbers. The only two elements in prime numbers are 1 and the number itself. Prime numbers include numbers such as 2, 3, 5, 7, 11, 13, 17, 19, and so on. Any number can be represented as a product of prime numbers when it is prime factored.

Prime Factorization using Division Method

By dividing a huge integer by prime numbers, you can get the prime factors. To find the prime factors of an integer using the division method, follow these steps:

Step 1: Divide the number by the smallest prime number in such a way that the smallest prime number entirely divides the number.

Step 2: Divide step 1’s quotient by the smallest prime number once more.

Step 3: Repeat steps 2 and 3 until the quotient is 1.

Step 4: Finally, multiply all the divisors’ prime factors.

Let’s use the division approach to prime factorise 60.

Prime factorization of 60 = 2 × 2 × 3 × 5
Hence, the prime factors of 60 are 2, 3, and 5.

HCF and LCM Tricks

Two or more numbers have an H.C.F that is less than or equal to the smallest number of supplied numbers.

L.C.M of a, b, and c is the lowest number precisely divisible by a, b, and c.

The greatest number of provided numbers is larger than or equal to the L.C.M. of two or more numbers.

In each example, the smallest number that leaves a remainder R when divided by a, b, and c. Required number = (L.C.M of a, b, c) + R

The greatest number which divides a, b and c to leave the remainder R is H.C.F of (a – R), (b – R) and (c – R)

The greatest number which divide x, y, z to leave remainders a, b, c is H.C.F of (x – a), (y – b) and (z – c)

The smallest number which when divided by x, y and z leaves remainder of a, b, c (x – a), (y – b), (z – c) are multiples of M

Required number = (L.C.M of x, y and z) – M

Conclusion 

The term “Least Common Multiple” is abbreviated as LCM. The smallest number that may be divided by both numbers is called the least common multiple of two numbers. It can be done with two or more integers or fractions.

To find the LCM of two numbers, there are several techniques. The product of the highest powers of the common prime factors is the LCM of those numbers, which is one of the easiest ways to find it. In mathematics, the least common multiple (or LCM) is referred to as the lowest common multiple. The smallest number among all possible multiples of two or more numbers is the least frequent multiple.

The largest possible number that splits both integers exactly is the highest common factor (HCF).

HCF represents the HCF of a and b. (a, b).

If d is the HCF (a, b), the common factor of a and b cannot be bigger than d.

The largest common divisor is another name for the highest common factor (HCF) (GCD)

The product of the least powers of the common prime factors is the HCF of those numbers, which is one of the easiest ways to find it.

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Frequently asked questions

Get answers to the most common queries related to the CAT Examination Preparation.

What is the easiest way to find HCF and LCM?

Ans. The highest common factor is found by multiplying all the factors which ...Read full

What is the formula of HCF LCM?

Ans. HCF and LCM Formula and Tricks ...Read full

How do you solve HCF short tricks?

Ans. Division Method to find HCF (Shortcut): ...Read full

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Ans. Tips and Tricks and Shortcuts to find HCF easily Solution: Find t...Read full

How to find HCF by Prime Factorization?

Ans. Step 1: Find the prime factors of the given numbers. In this case, the prime factors of 24 = 2 × 2 × 2 × 3,...Read full