LCM (Least Common Factor)

LCM means Least Common Factor

Find the LCM of 12, 18 and 24.

Method 1:

LCM = 2³ × 3² = 72

Method 2:

12 = 2² × 3

18 = 2 × 3²

24 = 2³ × 3

LCM = 2³ 2³ × 3² = 72

LCM is the product of highest power of each distinct factor.

Exercise:

1. Find the least number exactly divisible by 10, 12, 15, and 24.
2. Find the largest 3-digit number exactly divisible by 10, 12, 15, and 24.
3. Find the least 4-digit number exactly divisible by 10, 12, 15, and 24.
4. Find the least number which when divided by 12, 15, 20 and 27 leaves remainder 2 in each case.
5. Find the least number which when divided by 52 leaves remainder 35, when divided by 78 leaves remainder 61 and when divided by 117 leaves remainder 100.
6. What smallest number can be subtracted from 1000, so that remainder may be divisible by 24, 36 and 48?
7. Find the least square number which is divisible by 3, 4, 5, 6 and 8.
8. There are 5 bells which starts ringing simultaneously together at interval of 3, 6, 9, 12 and 15 seconds. In 36 minutes, how many times the bells will ring simultaneously?
9. Two men started moving on circular path from same place at same time in same direction. If they complete one rotation in 10 and 15 minutes respectively. After how long they will meet again?

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