LCM of 30 and 45

There are various methods to find the LCM, Listing method, prime factorization method, and division method are explained below; 

The LCM of 30 and 45 can be calculated using the following steps:

Step 1:Write down the multiples of each number

  — Multiples of 30 = 30, 60, 90,…

  — Multiples of 45 = 45, 90, 135,…

Step 2:Ascertain the smallest multiple from the listed multiples:

  — The smallest common multiple is 90.

Thus, LCM(30,45) = 90

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Step 1: Find the prime factors of each number:

  — Prime factorization of 30 = 2¹×3¹×5¹

  — Prime factorization of 45 = 3²×5¹

Step 2: Take the highest powers of each prime factor and multiply the highest powers to get the LCM:

LCM(30,45) = 90
 

This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors, and multiply the divisors.

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’ and bring down the numbers not divisible by the previously chosen prime number.

Step 3:The LCM of the numbers is the product of the prime numbers in the first column, i.e, 

2×3×3×5 =90

Thus, LCM(32,48)=90

• Prime Factor: A natural number (other than 1) that has factors that are one and itself.

• Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 

• Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 

• Relatively Prime Numbers:Numbers that have no common factors other than 1.

• Fraction: A representation of a part of a whole.