how to do L.C.M how to do
Answers
Answer:
L.C.M= Lowest Common Multiple.
Step-by-step explanation:
Lowest common multiple or LCM is the finding of the least common number that is multiple and divisible by the numbers you are using.
example: finding LCM of 50 and 25
we can see that 5 is both divisible by 50 as well as 25.
therefore the firstt multiple is 5.
dividing with 50 and 25, we are left with 10 and 5 respectively.
then again we can divide with 5
i.e, 10 divided by 5= 2 and 5/5=0
and 2 ones are 2 that divides the remaining 2.
therefore our LCM is= 5×5×2= 50
ans.= LCM of 50 and 25 is 50
Answer:
Though we have three methods to find the least common multiple, the division method is the most common and easy method that we use.
Step-by-step explanation:
We can find out the common multiples of two or more numbers by listing their multiples. Out of these common multiples, the least common multiple is considered and the LCM of two given numbers can thus be calculated. To calculate the LCM of the two numbers A and B by the listing method, we use the steps given below:
Step 1: List the first few multiples of A and B.
Step 2: Mark the common multiples from the multiples of both numbers.
Step 3: Select the smallest common multiple. That lowest common multiple is the LCM of the two numbers.
LCM by Prime Factorization Method
By using the prime factorization method we can find out the LCM of the given numbers. To calculate the LCM of two numbers using the prime factorization method, we use the steps given below:
Step 1: Find the prime factors of the given numbers by repeated division method.
Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.
Step 3: The product of these factors with the highest powers is the LCM of the given numbers.
Step 1: The prime factorization of 60 and 90 are: 60 = 2 × 2 × 3 × 5 and 90 = 2 × 3 × 3 × 5
Step 2: If we write these prime factors in their exponent form it will be expressed as, 60 = 22 × 31 × 51 and 90 = 21 × 32 × 51
Step 3: Now, we will find the product of only those factors that have the highest powers among these. This will be, 22 × 32 × 51 = 4 × 9 × 5 = 180
Therefore, LCM of 60 and 90 = 180.
LCM by Division Method
In order to find the LCM by division method, we divide the numbers by a common prime number, and these prime factors are used to calculate the LCM of those numbers. Let us understand this method using the steps given below:
Step 1: Find a prime number which is a factor of at least one of the given numbers. Write this prime number on the left of the given numbers.
Step 2: If the prime number in step 1 is a factor of the number, then divide the number by the prime and write the quotient below it. If the prime number in step 1 is not a factor of the number, then write the number in the row below as it is. Continue the steps until 1 is left in the last rows.
Step 1: 2 is the smallest prime number and it is a factor of 6. Write 2 on the left of the two numbers. For each number in the right column, continue finding out prime numbers which are their factors.
Step 2: 2 divides 6 but it is not a factor of 15, so we write the number 15 in the row below as it is. Continue the steps until 1 is left in the last row. Then, we divide 3 and 15 by 3. This gives us 1 and 3. Now, again we write 5 on the left side and we finally get 1, 1 as the quotient in the last row.
Step 3: Then we multiply these numbers on the left. The LCM is the product of all these prime numbers. LCM of 6 and 15 is, 2 × 3 × 5 = 30.