What is the LCM of 30 and 70?
To find the LCM of 30 and 70, we need the least number which is exactly divisible by both 30 and 70.
Answer: LCM of 30 and 70 is 210
The Least Common Multiple (LCM) of two numbers a and b is the smallest number that is divisible by a and b exactly.
We can find the LCM of the numbers in the following two ways.
Method 1: LCM of 30 and 70 by Listing Method
In this method, we list the first few multiples of 30 and 70 and identify the common multiples.
The least among the common multiples is the LCM of 30 and 70.
Multiples of 30: 30, 60, 90, 150, 180, 210, 240
Multiples of 70: 70, 140, 210, 280
Clearly, 210 is the least common multiple of 30 and 70.
LCM of 30 and 70 is 210.
Method 2: LCM of 30 and 70 by Common Division Method
Follow the steps mentioned below to find the LCM of 30 and 70 by the common division method.
Step 1: Write the numbers 30 and 70 horizontally by separating them with a comma.
Step 2: Choose the smallest prime number that divides at least any one of them.
Step 3: Write the quotient in the next row just below the numbers. If any of the numbers are not divided, we will bring it down directly.
Step 4: We will stop it when we don't have a prime number to divide the given numbers.
Step 5: Least common multiple of 30 and 70 will be the product of primes by which we have divided.
So, by common division method, we have LCM of 30 and 70 = 2 × 3 × 5 × 7 = 210
Observe that the solution to our question LCM of 30 and 70 is the same in both methods.