LCM of 30 and 42

The LCM of 30 and 42 is the smallest positive integer that is a multiple of both numbers. 
 

We can find the LCM using the listing method, prime factorization method and division method as explained below; 
 

The LCM of 30 and 42 can be found using the following steps

Step 1: Write down the multiples of each number: 

Multiples of 30–30,60,90,120,150,180,210,…

Multiples of 42–42,84,126,168,210,…

Step 2: Pick the smallest multiple from the multiples of 30 and 42. 

The LCM of 30 and 42 = 210
 

The prime factors of the given numbers are written, and the highest power of the prime factors is multiplied to get the LCM.

Step 1:  Find the prime factors of the numbers:

30= 3×5×2

42 = 2×3×7

Step 2 : Multiply the highest power of each factor to get the LCM. 

LCM (30,42) = 210

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

Step 1 : Write down the numbers in a row;

Step 2 :A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. Continue dividing the numbers until the last row of the results is ‘1’. Carry forward the numbers not divisible by the previously picked prime number.

   
Step 3 :The LCM of the numbers is the product of the prime numbers in the first column, i.e, LCM (30,42) = 210

• Multiple — It is a product of a number and any natural integer. So for 30,both 3,2 and 5 are the multiples.

• Prime Factor — It is a prime number that one gets after factorization of any given number. Like for 30, 2,3,5,6,15 and 30 are prime factors as they can be divided by 1 or the number itself.

• Prime Factorization — It is a process of dividing the number into prime factors.

• Co-prime numbers — These are the positive integers where both the numbers can be divided only by 1. 

• Fraction — It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 30/5 ,30 is the numerator and 5 is the denominator. Proper fraction is where numerator is always lesser than denominator.