Find their LCM of 36 and 54
Answers
Answer:
108
step by step: 2×2×3×3×3
= 108
Answer:
Step-by-step explanation:
LCM of 36 and 54
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LCM of 36 and 54 is the smallest number among all common multiples of 36 and 54. The first few multiples of 36 and 54 are (36, 72, 108, 144, 180, 216, . . . ) and (54, 108, 162, 216, 270, 324, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 54 - by prime factorization, by division method, and by listing multiples.
What is the LCM of 36 and 54?
Answer: LCM of 36 and 54 is 108.
LCM of 36 and 54
Explanation:
The LCM of two non-zero integers, x(36) and y(54), is the smallest positive integer m(108) that is divisible by both x(36) and y(54) without any remainder.
Methods to Find LCM of 36 and 54
The methods to find the LCM of 36 and 54 are explained below.
By Prime Factorization Method
By Listing Multiples
By Division Method
LCM of 36 and 54 by Prime Factorization
Prime factorization of 36 and 54 is (2 × 2 × 3 × 3) = 22 × 32 and (2 × 3 × 3 × 3) = 21 × 33 respectively. LCM of 36 and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 33 = 108.
Hence, the LCM of 36 and 54 by prime factorization is 108.
LCM of 36 and 54 by Listing Multiples
To calculate the LCM of 36 and 54 by listing out the common multiples, we can follow the given below steps:
Step 1: List a few multiples of 36 (36, 72, 108, 144, 180, 216, . . . ) and 54 (54, 108, 162, 216, 270, 324, . . . . )
Step 2: The common multiples from the multiples of 36 and 54 are 108, 216, . . .
Step 3: The smallest common multiple of 36 and 54 is 108.
∴ The least common multiple of 36 and 54 = 108.
LCM of 36 and 54 by Division Method
LCM of 36 and 54 by Division Method
To calculate the LCM of 36 and 54 by the division method, we will divide the numbers(36, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 54.
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 54. Write this prime number(2) on the left of the given numbers(36 and 54), separated as per the ladder arrangement.
Step 2: If any of the given numbers (36, 54) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 36 and 54 is the product of all prime numbers on the left, i.e. LCM(36, 54) by division method = 2 × 2 × 3 × 3 × 3 = 108.
