Question

by using prime factorisation method find the L.c.m of :15.30, 60 and 120​

Answer 1

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step 01::-Decompose all numbers into prime factors

15::-

• 15|3
• 5|5
• 1

30::-

• 30|2
• 15|3
• 5|5
• 1

60::-

• 60|2
• 30|2
• 15|3
• 5 |5
• 1

120::-

• 120|2
• 60|2
• 30|2
• 15|3
• 5|5
• 1

step 2. Write all numbers as the product of its prime factors

• 2. Write all numbers as the product of its prime factorsPrime factors of 15 = 3 . 5
• Prime factors of 30 = 2 . 3 . 5
• Prime factors of 60 = 22 . 3 . 5
• Prime factors of 120 = 23 . 3 . 5

step 3. Choose the common and uncommon prime factors with the greatest exponent

• . Choose the common and uncommon prime factors with the greatest exponentCommon prime factors: 3 , 5
• Common prime factors with the greatest exponent: 31, 51
• Uncommon prime factors: 2
• Uncommon prime factors with the greatest exponent: 23

Step 4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 31. 51. 23 = 120