Least Common Multiple

Slide 1 : LEAST COMMON MULTIPLE By : Monali Thakur monali_253@yahoo.co.in

Slide 2 : What is LCM? A NUMBER WHICH IS A MULTIPLE OF TWO OR MORE NUMBERS IS A COMMON MULTIPLE OF THESE NUMBERS. THE SMALLEST OF THE COMMON MULTIPLES OF TWO OR MORE NUMBERS IS CALLED THEIR LEAST COMMON MULTIPLE OR LCM

Slide 3 : Simply list the multiples of each number (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list. Example: Find the least common multiple for 5, 6, and 15. First we list the multiples of each number. Multiples of 5 are 10, 15, 20, 25, 30, 35, 40,... Multiples of 6 are 12, 18, 24, 30, 36, 42, 48,... Multiples of 15 are 30, 45, 60, 75, 90,.... Now, when you look at the list of multiples, you can see that 30 is the smallest number that appears in each list.  Therefore, the least common multiple of 5, 6 and 15 is 30. METHOD -1

Slide 4 : METHOD – 2 :LCM by prime factorisation Example : Find the LCM of 54 and 90 54 = 2 x 3 x 3 x 3 90 = 2 x 3 x 3 x 5 First take the common factors of both the numbers. Common factors = 2 x 3 x 3 Next, take the other numbers which are unpaired. Unpaired factors = 3 x 5 Multiply both together LCM = 2 X 3 X 3 X 3 X 5 = 270. 54 90 2 3 3 3 27 9 3 1 2 45 3 15 3 5 5 1

Slide 5 : Find the LCM of 120 , 252 and 550 (by prime factorisation method)

Slide 6 : METHOD -3 : LCM by Division Method First , we write all numbers in a row separated by a comma. Then, we find a prime number which must at least divide minimum two numbers if not all at a time. Then, we write the quotients (obtained after dividing) immediately below the numbers in the second row. The undivided numbers are written as it is. We then again, find a prime number which at least divides two numbers in the second row. The quotients and undivided numbers are brought down to the third row. We continue this procedure till no two numbers in the last row are divisible by any number. Then, we multiply all the divisors and the left over undivided numbers in the last row. Their product gives us the LCM of the given numbers. The above method is only suitable when the given numbers are small.

Slide 7 : Example : Find the LCM of 20 , 36 , 48

Slide 8 : Find the LCM of 112, 126, 336

Slide 9 : Find the LCM of 96 , 144 , 164

Slide 10 : Relationship between HCF and LCM HCF X LCM = First number x Second number

Slide 11 : The LCM of two numbers is 21 and their HCF is 1 . If one of the numbers is 3, what is the other number?

Slide 12 : The product of two numbers is 40. The numbers are co-prime. One of the numbers is the first multiple of 5. What is the other number?

Slide 13 : I can make packets of 6 sweets or 8 sweets or 10 sweets. What least number of sweets must I have so that I can put them in any of the grouping mentioned above without leaving any sweet?

Slide 14 : Find the HCF and LCM of 25,105

Slide 15 : NOW HAVE A LOOK AT THIS !!!!!

Slide 16 : When a divisor divides a number such that there is no remainder left, then the divisor is called the factor of the dividend and the dividend is called the multiple of the divisor. e.g. 24 divided by 6 = 4 24 divided by 4 = 6 Thus, 6 and 4 are factors of 24 and, 24 is a multiple of 6 and 4.

Slide 17 : All the multiples of 2 are even numbers Numbers which are not multiples of 2 are odd numbers.

Slide 18 : Prime numbers Numbers which have only two factors ( 1 and the number itself) are called prime numbers. e.g. 2,3,5,7,11,13,17,19…..

Slide 19 : Composite numbers Numbers which have more than two factors are called composite numbers. e.g. 4,6,8,9,10,12,14,15…….

Slide 20 : 1 is a unique number. It is neither prime nor composite , as it has only factor. Also , it is a factor of every number.

Slide 21 : Two numbers whose HCF is 1 are called co-prime numbers. They need not be prime nos. e.g. 9 ,10 15,28

Slide 22 : Two prime numbers whose difference is 2 , are called twin prime numbers. e.g. 3,5 5,7 17,19 29,31

Slide 23 : Every number has a fixed number of factors. Whereas, Multiples of any given number are unlimited.

Slide 24 : Which is the only even number which is a prime number?

Slide 25 : Any Doubts ????

Slide 26 : Thank you !!!!!!!